The former Preston and Sheffield Wednesday boss is keen to add to his squad and West Brom have emerged as contenders to beat Hull to the defender's signature.
Manchester City paid Everton £22m for his services in August 2009 but Manuel Pellegrini deemed him surplus to requirements at the Etihad and released him at the end of last season.
“There is an interest in Joleon and he is a player I know well,” Irvine told a media conference.
“I obviously worked with him at Everton and I remember there were a number of times we watched him.
“Coincidentally, I saw him towards the end of the season when Manchester City played Everton. I had a chat with him then but, of course, I didn’t know any of this was happening at the time.”
Irvine was a surprise appointment to replace sacked Pepe Mel at the Hawthorns and the Scot was also keen to appease supporters unhappy at his appointment after leaving his role as Everton’s academy boss.
“It would be lovely if everyone was absolutely delighted in thinking this is the best appointment that can be made but the only way I can prove that is to help the team to get success,” he said.
“Every manager will be judged by the results they get on the pitch and unfortunately that cannot happen for a number of weeks because we are not playing any league games.
“But that gives me a bit of time to work with the players, try and get the squad together and be ready for the start of the season.”
Irvine will begin his Premier League reign against Sunderland at home on the opening day of the new season.