The Italian is favourite to replace Remi Garde at Villa Park.
Villa, who will play in the Championship next season following their Premier League relegation, have been without a manager since March 30 when it was announced that Remi Garde had been sacked.
Caretaker Eric Black taken charge of the team since then but if anything things have gotten worse, with the Villans winning one point from a possible 18 since the Frenchman - who had won one game out of seven prior to being sacked - left the club.
With the summer transfer window upon us, ideally Villa fans would want a new manager in as soon as possible in order to shape his squad ahead of what promises to be an arduous 46-game Championship season.
Nigel Pearson had been favourite for that role, but Di Matteo, who has been out of work since leaving Schalke at the end of last season, is now 5/4 favourite according to Sky Bet - and a lot of Villa fans didn't react kindly to the news.
@Avillafan W T F,that's gotta be the daftest yet,how about that other famous Roberto we nearly had ,at least he's got champ experience— andy young (@misterbdisco) May 11, 2016
Please NOT Di Matteo! No no no. Pearson is the man #AVFC— Richard Armstrong (@RicardoAVFC) May 11, 2016
The 45-year-old led West Brom to Premier League promotion in 2010, before being fired midway through their return to the top flight. One year later, he replaced Andre Villas-Boas at Chelsea, later guiding the Blues to their first ever Champions League title, but was dismissed by Roman Abramovich not long after winning a long-term contract.