The club are reluctantly preparing to act in the next 24 hours following their awful start to the season, Press Association Sport understands.
Saturday's 2-0 defeat at Preston left Villa 19th in the Sky Bet Championship with just one win from their opening 11 games and only two points clear of the relegation zone.
The club spent around Â£50million in the summer, including Â£12million on Ross McCormack and Â£15million on Jonathan Kodjia, to ensure an instant return to the Premier League.
But owner Tony Xia, who bought the club and appointed Di Matteo in the summer, is now losing patience with Villa 15 points behind leaders Huddersfield
Villa were hopeful Di Matteo would lead them back to the top flight after they were relegated last season, winning just three games, but they have continued to fall this term
They have dropped 11 points from goals conceded in the last five minutes with Di Matteo's only win a 3-0 victory over Rotherham in August and he has drawn seven of his 12 games
Villa also suffered a shock 3-1 defeat in the EFL Cup to League Two side Luton.
Should the former West Brom and Chelsea manager depart as expected Villa will be looking for their fifth permanent boss in just over two years with Paul Lambert, Tim Sherwood and Remi Garde all leaving since February 2014.
Ex-Hull manager Steve Bruce and Brentford boss Dean Smith, a boyhood Villa fan, have already been linked to the job.
Source : PA