The 34-year-old is reportedly in the process of negotiating an early release from his Villa contract.
Cole, 34, initially joined Coventry in mid-October on a 35-day emergency loan which was later extended until the New Year and has since made seven League One appearances for the club, while recording one goal and an assist.
The former England international’s Villa contract expires in the summer and he is now said to be negotiating an early release from his deal in order to allow him to join the Sky Blues on a permanent basis.
Coventry boss Tony Mowbray has already confirmed that Cole will have to take a hefty wage cut to make the move possible, telling the Coventry Telegraph: “I think the player will help us but there’s a number of discussions to be had, not just with our football club and the clubs concerned.
“There’s no way we could pay similar sorts of salary levels so they’ll have discussions with their parent clubs and after that we need to have discussions with their advisors. So there’s lots of stuff to be talked about.”
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Cole originally joined Villa on a two-year deal in June 2014 after being released by West Ham United but a series of nagging injuries restricted him to five starts in 15 total appearances during his first season in the Midlands.
The former Chelsea and Liverpool midfielder managed to get a full pre-season under his belt ahead of this term but earned just one 60-minute run-out off the bench in the 5-3 Capital One Cup second round win over Notts County during the opening months of the campaign before eventually linking up with Coventry.
His move down to League One came as somewhat of a shock at the time, but the three-time Premier League winner has so far relished the chance to get regular minutes amid the club's promotion push.
"I want to be playing, I'm fit, and it suited everybody concerned,” Cole told Sky Sports in December. “It was a good move and I'm really enjoying my time there. I've always been advised to play on for as long as I can, and if the body is still telling me to play, I'll keep doing it and I'm enjoying it.
"It's exciting to be in a team winning games at the right end of the league, which I haven't for a long time. It's been an eye-opener."