The 31-year-old will leave the Etihad Stadium when his contract expires at the end of June and had been strongly linked with a move to Hull City as Steve Bruce looks to bolster his squad for next term's Europa League campaign.
|3/1||West Brom are 3/1 with PaddyPower to be relegated from the Premier League|
Speaking at his unveiling to the press after replacing Pepe Mel, Irvine confirmed: "There is an interest in Joleon.
"He is someone I know well. I had a great working relationship with him in the past.
"I believe negotiations are going well. Hopefully we're able to meet Joleon's demands. That's the calibre of player we would like to bring in.
"We are not there yet but there's an interest."
Irvine previously worked with Lescott at Everton when he was assistant to then-Toffees manager David Moyes.
Lescott was signed by City from Goodison Park in a £24 million deal in 2009 but made just 10 Premier League appearances last term after slipping behind Martin Demichelis and Matija Nastasic in Manuel Pellegrini's pecking order.