Lescott, 31, will leave the Etihad Stadium when his contract expires at the end of the month and had been strongly linked with a move to Hull City as Steve Bruce looks to bolster his squad for next term's UEFA Europa League campaign.
However, West Brom have signalled their intent to snatch Lescott - who began his career at fierce rivals Wolves - from under Hull's noses.
Speaking at his unveiling 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. I've had a great working relationship with him in the past."
Irvine has previously worked with Lescott at Everton when assistant to 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.
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