Asked where she was off to, Eliza told the award-winning photographer: "I'm going to Farmfoods."
Murphy found out where she lived, knocked on the family's tenement flat window and spoke to her mother.
He then set up his tripod, adjusted his medium format camera and captured a striking street portrait.
It is now one of more than 150 black and white images which feature inGovanhill, a new exhibition celebrating one of Scotland's most diverse communities.
An estimated 88 languages are spoken in the densely populated area, which covers about a third of a square mile or 85 hectares.
The community has been close to Murphy's heart since his grandmother moved there from the nearby Gorbals in the early 1970s.
It has even been compared to New York's Ellis Island, as a point of arrival for immigrants who travel to Glasgow seeking a better life.
The photography lecturer told BBC Scotland News: "People used to say there were two sides to Govanhill - Bengal and Donegal.
"It is a real melting pot of different nationalities and cultures."
In 1999 Murphy rented a flat in the area before taking on his first job, as a postman in nearby Clarkston.
He later sold his guitar to buy his first camera in Cash Converters for Â£50 before enrolling on a photography course in the city's Springburn.
Since then he has spent more than two decades taking pictures of Govanhill residents and people who were simply passing through.
Asked how he selects his subjects, Murphy said: "It's all about wandering. I might see someone who looks a bit interesting.
"It's definitely a visual thing. It could be a haircut, a guy who looks craggy or something slightly off kilter."
The father-of-two started his street portrait project in 2016 and, during the Covid lockdown, he created a window trail exhibition featuring 25 images.
One of his most celebrated pictures features Paisley, whom he met with her young son in McDonalds.
He said: "She was wearing a camouflage jacket and had amazing hair.
"Paisley featured in my first exhibition and came to represent the project.
"She has a 'People Make Glasgow' badge and there is an attitude, a defiance and a strength there that I feel sums up the people of Govanhill."
In Sara's case it was her over-sized fur coat that caught his eye.
Murphy recalled: "It looked amazing and it turned out it belonged to her mum.
"Sara was popping out to the shops and when shops are so close by people sometimes grab the first thing that is lying at the door.
"I imagine that the mum's coat was the closest thing to hand.
"I loved it and thought it made Sara look very regal, queen-like."
Murphy has become so embedded in the community that he has even photographed some of his subjects on more than one occasion.
This was true of the girl who took her cat shopping.
But he only discovered the coincidence when he spoke to Eliza's mother.
Murphy recalled: "She told me I had photographed her daughter four years earlier, when she was going to a party with her sister.
"They had just got out of a taxi and were wearing beautiful dresses and were clutching huge presents wrapped in LOL doll paper.
"I crossed the street and asked if their parents were around so I could get permission but it turned out their dad was the driver and he agreed."
Last year Eliza again found herself in front of Murphy's Mamiya R267 camera.
He said: "She had shopping to do but allowed me the time to capture a few frames and I tried to get the cat to look towards camera too.
"When I went around to the house to drop off a print, Eliza's mother was so happy. She told me: 'You don't know what this will mean to Eliza'."
She went on to explain that the cat had since gone missing.
Murphy added: "This was the only photograph that she had of her and her cat together and it meant the world to the family."
Tattoo artist Scott took some persuading to pose. The photographer succeeded because Scott's wife was a customer of his wife, Beth, who used to run a nail salon in Govanhill.
Murphy said: "Scott said he wouldn't normally do it but let me take his picture.
"He looks like an intimidating character but if you look really closely you see what matters to him.
"Above his right eye he has the word 'family' tattooed.
"There is a softness there. We don't spend a lot of time looking at people's eyes."
When Murphy first encountered performance artist Seamus he had recently lost his elaborate costumes in a fire.
But the next time they caught up he was dressed as a giant rat.
Murphy, who is a lecturer at Glasgow Kelvin College, said: "He was quirky and playing a character.
"The ideas that Seamus comes up with and brings to life could form a whole project on its own.
"It was tongue-in-cheek as the area has been portrayed as having a rodent problem.
"Govanhill does have issues, and I'm not aiming to hide or amplify them, that's not my job.
"But if you look properly, you will find treasure in Govanhill and that treasure is its people."
Murphy's previous work with The Herald newspaper and as a freelance included assignments in Colombia, South Sudan, the Democratic Republic of Congo and Ethiopia.
More recently he chronicled the harrowing plight ofRohingya refugeesin Bangladesh on a trip with aid agency SCIAF.
Reflecting on his personal journey he said: "I loved David Bailey's pictures of The Beatles and The Rolling Stones and was drawn in by the celebrity culture.
"But when I started travelling my priorities shifted. Photography opened my eyes.
"It gave me a greater empathy and understanding of what is going on in the world and the difficult lives people have.
"I really think it shaped me. I became less interested in celebrities and just photographing real people."
Murphy's passion for the traditions of his craft in the age of digital also makes his raw portrait work stand out.
He said: "I use medium format film, which gives the images a lot of clarity and sharpness, even when they are blown up.
"It is the type of film that was used for photographing movie stars in the past and it gives them a timeless quality.
"The street is my studio and I want people to be proud of their pictures."
Govanhill runs at Street Level Photoworks in Trongate, Glasgow, until 27 January
Simon Murphy was standing on Victoria Road, in the bustling south side of Glasgow, when he spotted a girl walking towards him with a cat round her neck.