Clarke was dismissed after Saturday's 1-0 Barclays Premier League defeat at Cardiff City, the Midlands club's fourth straight loss, and McInnes's candidature has been given a positive reception by a leading WBA fans' representative.
Alan Cleverley, WBA supporters' club secretary, feels reappointing former manager Roberto Di Matteo, the bookmakers' favourite, or former player and ex-Fulham manager Martin Jol, would not be best for the club. He said: "If it's Jol, it is someone else's cast-off, while Di Matteo has done it before and wasn't a great success in the Premier League with us. I haven't seen a name yet where I think to myself 'yes, that would be fine'.
"I wouldn't want an inexperienced manager coming in. Derek McInnes could be interesting. But I'd really like someone who has managed at a high level, even if he comes in from abroad.
"If you are trying someone out at this level, you might as well stay with Steve Clarke because if they are new to it, they could make a few mistakes and before you know it you are bottom of the league. If you get someone who has managed in the top leagues abroad, they are going to be used to the pressure."
Di Matteo, who guided West Brom into the top flight in 2010 but was relieved of his duties in February 2011, and ex-Albion player Jol are among those being mentioned, along with McInnes, Molde manager Ole Gunnar Solskjaer, and former Schalke manager Ralf Rangnick.
Clarke left with West Brom 16th in the table, two points above the relegation zone and having won seven of their 34 top-flight matches in 2013. The 50-year-old was appointed in the summer of 2012.
Cleverley said: "I would have given him a little bit longer, but coming back from Cardiff on Saturday I would have said the coach was split about 50-50. It is not like we're adrift at the bottom, and the guy took us to eighth last year, which is overachieving."