The 31-year-old will become a free agent next month when his contract with Manchester City expires.
He had been strongly linked with a move to Hull City, but having worked with Lescott during the pair's time together at Everton, Irvine has expressed his hope that they will be reunited at The Hawthorns.
"There is an interest in Joleon. He is someone I know well. I had a great working relationship with him in the past," he told reporters.
"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."
Lescott made just 10 Premier League appearances for the Citizens last term.