Unison said in a dossier sent to Carillion, the company responsible for cleaning, that improvements need to be made at Nottingham City Hospital.
The hospital trust said a kitchen had reopened following a deep clean and there had been no "increase in infections" prior to this.
Carillion said it was working with the trust to "address outstanding issues".
Corall Jenkins, regional organiser of Unison, said the rat was seen on 7 and 8 August in a kitchen on a ward.
She said photographs taken in the hospital since the deep clean raised further issues.
"These pictures don't demonstrate an improvement in the standards of health and hygiene as borne out by our members concerns," she said.
"Staff are having to bring their own cleaning materials to work because of a lack of supplies.
"Improvements must be made as a matter of urgency."
Carillion won the five-year contract for cleaning, laundry and catering services in 2014.
In July, hospital bosses said the cleaning contract could be terminated if standards did not improve.
In a statement, Nottingham University Hospitals NHS Trust confirmed a kitchen was closed, deep cleaned and has since reopened following the "alleged vermin sighting".
"The trust is monitoring Carillion's performance monthly, and is very carefully considering the future of the contract with Carillion."
In a statement, Carillion said: "We have received a document from Unison which makes a number of claims relating to our contract with Nottingham University Hospitals.
"The claims will be fully and fairly investigated, and, if we find there is any substance to any of them we will take corrective action."
A union has called for an urgent review into cleanliness after a rat was apparently seen in a hospital kitchen.