The 25-year-old claims Arsene Wenger has sent Gunners scouts to watch him in every match he's played this season.
The report claims he's been scouted by several top clubs, and Ahmedov has now confirmed he believes Arsenal are one.
"It is true I have interest from Arsenal - their scouts have watched me in every match this season," Ahmedov told Izvestia.
"If I move there, I could be a huge success but there is no bid yet."
The Uzbekistan international joined the big-spending Russian giants from Pakhtakor Tashkent in 2011.
And he's scored two goals in 60 league appearances for Anzhi, although he primarily plays as a defensive midfielder.
Arsenal are believed to be looking at him as a replacement for Alex Song, who departed for Barcelona last summer and was not replaced.
Abou Diaby has struggled to overcome long-term injury problems, while Denilson has been released.
That leaves Wenger with Aaron Ramsey, Tomas Rosicky, Mikel Arteta and Jack Wilshere in midfield, but none of the four is a natural holding midfielder.