The 63-year-old, who already owns 30% of the club, is said to have tabled the mammoth offer to tempt Kroenke into selling up.
It is claimed by the Financial Times that Usmanov wrote to Kroenke last month to express his interest in taking control of the Gunners, but the American business entrepreneur has yet to respond.
A source is quoted by the publication as saying: "Two weeks ago, I thought something could realistically happen. Now I am not so sure."
Usmanov, worth more than £11bn, has previously clashed with Kroenke over a lack of investment on his counterpart's behalf.
The attempt to take full control at the Emirates Stadium could also have a knock-on effect to Arsene Wenger's decision to stay on, with Usmanov a firm supporter of the long-serving boss.