Osmanov has 30 percent of Arsenal's shares, but he is not a member of the club's board and does not participate in making decisions.
Osmanov blamed Crock last month for the club's poor position in the Premier League and the Champions League, saying he "should have borne a great deal of failure in the team."
Their chances of reaching the Champions League next season were almost nonexistent before the last round of the Premier League.
The fans blame most of the French manager Arsene Wenger for demanding departure, saying he has "gone bankrupt and has nothing to offer the team technically" after more than 20 years in office.
The Arsenal board is due to announce their decision on Wenger after meeting Chelsea in the FA Cup final on the 27th of this month.
Osmanov is demanding more investment in the team, the purchase of outstanding players and the hiring of a technical director who can push the team to perform better and compete for bigger tournaments in England and Europe.
There has been news over the past few days that if Croenque refuses Osmanov's offer, the latter will withdraw his investment from Arsenal and lead him to another Premier League team, Everton, based in Liverpool.