The Ivorian has been out of favour at B6 since their promotion to the Premier League, and despite the season-ending injury suffered by Wesley early this month, looks set to depart Villa in the coming days.
Al Gharafa SC tweeted a picture of the 30-year-old arriving in Doha to sign for the club, with Villa yet to sign a replacement.
Kodjia has missed the last two games through illness, and will not be a part of the side making the trip to take on Brighton this weekend.
Dean Smith's side are nearing the signing of Mbwana Samatta, with the Tanzanian striker considered the club's number one target this month - however, he's unlikely to be available for the clash with the Seagulls as his deal is still to be confirmed and likely subject to a work permit being granted.
Reports in France claim that the deal for Kodjia could be worth up to €3m. The Ivorian has just six months remaining on his current Villa deal.
Meanwhile, it's understood that Islam Slimani is unlikely to leave Monaco this month, after Leicester City boss Brendan Rodgers claimed that a deal to recall the striker and loan him to Villa would be 'too complicated'.
Villa were linked with the Foxes forward, currently on-loan at Monaco - but Rodgers believes a deal would be hard to complete.
"That looks like it’s probably going to be too complicated." Rodgers told LCFC Live.
"There is an interest in him but he’s due to be at Monaco for the season so I’m not sure if anything would happen on that. It just may be a little bit complicated."
Christian Benteke also seems likely to stay put at Crystal Palace this month, with Roy Hodgson labelling reports of the Belgian departing as 'ludicrous'.
"I can’t believe I am being asked the question," Hodgson told football.london.
"I can’t believe someone is going to suggest - when we have very few forwards anyway - that we are considering loaning out a player who we are badly missing because he has been out injured, and that we as a football club, or I as a coach, are seriously considering loaning out what is potentially one of our best players.
"I find it hard to believe. When I ask a question I sometimes wonder if it is worth asking, because I know the answer, but we have to answer these questions.
"It is not quite as ludicrous as Wilf Zaha being loaned to Bayern Munich, but it is about ten per cent less ludicrous than that."
Should Villa fail to sign a striker before the weekend, Dean Smith will once again be forced to play without a recognised senior striker, with youngster Indiana Vassilev the only forward option available for selection due to Keinan Davis' ongoing injury problems.
Anwar El Ghazi has filled in at striker over the past two games, against Leicester and Manchester City.