The former Hibernian chief faces stiff competition for 24-year-old Elliott's signature, though, with Premier League duo Blackburn and Wolves believed to be lining up summer bids for his services.
Former Albion enforcer McInnes, meanwhile, has revealed he hopes Ferguson heads to The Hawthorns this summer as he feels he could rejuvenate his career having fallen out of favour under Walter Smith at Ibrox.
The 31-year-old watched Albion's defeat by Liverpool towards the end of the Premier League season and is believed to have already held talks with Mowbray about moving to the Black County.
And St Johnstone manager McInnes is hoping the deal comes off, saying: "I know it's not been the best year for Barry but he would be a fantastic signing for West Brom, not least because of how they play.
"He'd fit in perfectly with Tony Mowbray's playing style. He's a leader and a winner.
McInnes, who was a fans' favourite at The Hawthorns, added in the Birmingham Mail: "The good thing about Barry is that he does different jobs from midfield.
"The main thing is he can influence games wherever he plays.
"He'll score you goals, he can dictate play if that's where you want to play him.
"But I think he's best as a deeper player where he can make things happen.
"He's the kind of player who will demand responsibility on the ball and want it all the time.
"West Brom fans will take to him. I think he'd do a good job for them if he signed."