The 63-year-old currently owns 30 per cent of the club through Red & White Holdings and Press Association Sport understands a formal bid was made for Kroenke's shares but it is believed the American is expected to reject the offer
Usmanov has been a shareholder at the Premier League club since 2007 and upped his stake from 14.6 per cent to 30 when he bought out Farhad Moshiri in 2016.
He has a fractious relationship with Kroenke and last month he claimed that the club's issues should not be placed solely at the door of manager Arsene Wenger.
"I do not think that the coach alone is to be blamed for what is happening," he told Bloomberg - adding that the board, and main shareholder (Kroenke) "bear huge responsibility."
The Gunners face a multi-million pound drop in revenue if they fail to qualify for next season's Champions League.
They face Everton in the final round of Premier League matches on Sunday and need to win, with other results going their way, if they are to finish in the top four.
Despite the prospect of making a large profit, Kroenke appears to not want to sell.
That does not mean Usmanov has been put off and he could yet return with an increased bid - with Forbes currently listing his wealth at Â£11.2bn.
Former Arsenal striker Ian Wright says something has to change at the club.
"He (Usmanov) has put in the bid and it is great news," Wright told BBC Radio 5 live.
"Something has to change, whether it is the manager Arsene Wenger or whether it is the board upstairs.
"It is not looking good at the moment
They may be out of the Champions League - something they are not used to - and they have to beat one of the best Chelsea sides I have seen for a long time in the FA Cup final to try and get something from the season."
Meanwhile, Wenger has revealed his future will be finalised after next week's FA Cup final.
The 67-year-old has just two matches remaining before his current contract expires but has yet to announce publicly if he will sign fresh terms to remain at the Emirates Stadium.
Asked when the board meeting is scheduled for, Wenger replied: "I think it is after the FA Cup final."
When pushed on whether that is when a decision on his future will be finalised he said: "Yes.
"You have certainly to know that there are many aspects of a football club which have to be discussed at a board meeting.
"One of them is, of course, what is happening with the manager, the future, the players who have to come in, the renewal of contracts
You don't miss problems in a board meeting.
"Of course I will be there
At the moment I think we should focus on short term and what's going on on Sunday and in the cup final."
Source : PA