Spain star Villa is being lined up to replace Didier Drogba and Andriy Shevchenko.
But boss Grants future is not secure despite the fact they are in the title race and into the Champions League semi-finals.
Chairman Bruce Buck, asked if Grant would be boss next season, said: I think it is a yes or no question and I am not going to give you a yes or no answer.
Avram has a multi-year contract and hes our manager. Having said that, every manager, at every club, is judged by results.
Buck made his comments just a day after chief executive Peter Kenyon insisted the team had some way to go before playing the kind of football owner Roman Abramovich has demanded.
Grant has presided over the Carling Cup loss to Spurs as well as the humiliating FA Cup exit at Barnsley.
Buck stops with results
Buck added: We thought that when you change managers, you have to have some re-building. So we are unbelievably happy that we are here, where we are now.
We wished we would have beaten Barnsley and Tottenham and whatever, but I think we are reasonably happy with where we are now.
Thats the name of the game, results, and right now Avrams results are very good, so hes our manager.
The Blues are still planning ahead and are resigned to losing Drogba while Shevchenko is expected to return to AC Milan.
And Villa is their No 1 target to play up front alongside Nicolas Anelka next term.
Contact has already been made with the 26-year-olds representative, who confirmed Villas desire to play in the Premier League.
The Spain international was originally wanted by Jose Mourinho two seasons ago.
Valencia refused to sell then but with the club struggling in 14th position in La Liga, they are now prepared to cash in to rebuild the squad.
Villa has averaged a goal every two games for his club this season despite their faltering form.
And with Drogba expected to join Inter Milan should Mourinho go there as coach or Real Madrid, they need to recruit.