The duo have been tussling for Gunners shares for a number of years, with Kroenke currently owning the majority of the club with his 62% stake compared to the 30% held by the Uzbek investor.
Usmanov, who has been critical of the club's transfer policy in the past, denied reports claiming that he was willing to sell his shares and wants Arsenal to sign some top-class players.
"The team has no superstars now," Usmanov told The Mirror, adding that that Kroenke "would probably be happy" with a fourth-placed finish this season.
"In our understanding, Kroenke has no plans to sell his stake, but we also won't sell out, as we are the team's fans."
Usmanov recently climbed to the top of the Sunday Times Rich List for 2013.