Makelele, 44, is set to become a permanent part of Swansea's coaching team having joined manager Paul Clement's staff in January.
The former France international won two Premier League titles during his five seasons at Stamford Bridge.
"When he came to Chelsea it was all about him," Cork said.
"He is someone we really looked up to."
Midfielder Makelele was a key member of the Chelsea side who secured their first Premier League title under Jose Mourinho in 2005.
Cork was 15 at the time and a member of the Stamford Bridge club's youth set-up.
He was a ball-boy at Chelsea's final home game of the 2004-05 season against Charlton when the Blues were presented with the Premier League trophy.
"I always remember that they gave him a penalty because he hadn't scored for Chelsea," Cork said.
"The crowd were up for it and he missed it.
"He scored the rebound with a header, but I always remind him about that.
"Everyone talks about N'Golo Kante, but when Chelsea played 4-3-3 with Claude in the team, it became the Makelele role.
"When Claude was there, he had Frank Lampard, Didier Drogba and players like that and he probably went under the radar a bit, but you could not take him out of the team."
Swansea spent the season deep in relegation trouble, before eventually securing survival with one game to spare.
Cork acknowledged, before Sunday's final game against West Brom, that a campaign in which Swansea had three managers has been "difficult".
"I have been relegated before when I was with Burnley, but I was only on loan so it is different when you are part of a team," Cork added.
"So I probably say it would be the most difficult year so far because we knew we were capable of so much better.
"It was dangerous at times and hopefully it will not happen again."
Swansea City midfielder Jack Cork says he "looked up" to the club's assistant manager Claude Makelele during his time as a youngster at Chelsea.