The 23-year-old has made more than 150 league appearances for the Russian outfit, as well as making 33 outings for his country, helping Guus Hiddink's side reach the semi-finals of Euro 2008.
As a result, reports have surfaced linking the glove-man with a move to Sir Alex Ferguson's side, who have also been linked with Schalke stopper Manuel Neuer, as a replacement for 38-year-old No.1 Edwin van der Sar.
According to Moscow publication Sport Express, Bayern Munich are keen on recruiting the highly-rated shot-stopper, while Arsenal are also believed to be monitoring the youngster's progress.
But Akinfeev has revealed that, should they come calling, it would be difficult to say no to last season's Champions League runners-up.
"CSKA is a great club but every player would love to prove their worth at United," he said in The Sun.
