Baggies head coach Clarke was dismissed on Saturday following a 1-0 Barclays Premier League defeat at Cardiff, the midlands outfit's fourth straight loss.
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, recently dismissed from his post as manager of Fulham, are among those being mentioned as potential candidates to fill the vacancy, with the former installed as the bookies' favourite.
But regarding those options, West Brom supporters' club secretary Alan Cleverley told Press Association Sport: "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'."
After losing his job at West Brom, Di Matteo had a spell in charge at Chelsea that lasted from March to November 2012, during which the Blues won the Champions League and the FA Cup.
When it was put to him that Di Matteo had enjoyed considerable success since his stint with Albion, Cleverley said: "He has, but I wonder why nobody else has gone for him since then?
"He might be favourite, but that one would surprise me more than anything."
Also being tipped as contenders are the likes of Molde boss Ole Gunnar Solskjaer, former Schalke manager Ralf Rangnick and Aberdeen boss Derek McInnes, another ex-West Brom player.
Asked about Solskjaer - who, like Clarke was at West Brom, is in his first senior managerial job - Cleverley said: "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."
Clarke departed with West Brom 16th in the table, two points above the relegation zone and having won only seven of their 34 top-flight matches in 2013.
The 50-year-old Scot - under whom Albion achieved their highest Premier League finish of eighth last term - was appointed as their boss in the summer of 2012.
His deal with the club was due to run out at the end of this season and only late last month West Brom announced they planned to hold contract talks with him in the new year.
Cleverley said: "Personally, 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 on that.
"Some were for sacking him straight away. It really is a mixed one.
"I would have certainly seen it through to the end of the calendar year.
"It is not like we're adrift at the bottom and the guy took us to eighth last year, which is overachieving."
Asked if he was disappointed by the decision to sack Clarke, Cleverley added: "It is always difficult to say whether the chairman (Jeremy Peace) has been too ruthless, because in a few months' time if we are happily stuck in the middle of the Premier League I'd say he acted correctly and at the right time."
West Brom lost the services of their top goalscorer over the summer when Romelu Lukaku's loan spell with them ended and the attackers Albion brought in during the last transfer window are yet to truly impress.
In the latter contest, the hosts only drew level through a controversially-awarded penalty in stoppage time and Clarke later said he had received an apology from referees' chief Mike Riley.
Cleverley feels officials' decisions were key to Clarke's fate.
"We lost Lukaku and to replace him was very, very difficult," Cleverley said.
"But you can argue another case regarding referees' decisions at Stoke, when we drew 0-0 and might have won with a penalty that should have been given, and at Chelsea.
"You put four points on top of what we have got and we are higher up the league and he wouldn't have been sacked.
"That has nothing to do with football, tactics or players - it is to do with referees' mistakes. And I hope there are one or two referees today thinking 'did we contribute to Steve Clarke's downfall?' - because they did.
"It's alright them apologising afterwards, but that is no good to a bloke who is now out of work.
"I hope some of them phone him up and say 'sorry - I hope everything goes alright'."