Usmanov recently increased his stake in the Premier League club to around 21% via Red and White Holdings Limited, while Kroenke owns just over 12%.
The Gunners currently top the Premier League, but it is the recent activity on the stock markets which have grabbed the headlines.
Reports in the Russian media last week quoted Usmanov as being ready to up his interest to obtain a "blocking stake" of just over 25% before then waiting for the share price to "go up in value".
Managing director Keith Edelman said: "I am unsure what he [Usmanov] can do with 25%, and I do not believe he can stop us operating the business on a day-to-day basis.
"Usmanov has a stake, Kroenke has a stake and we get on and run the business every day.
"It is a distraction for us to keep talking about it, but we are trying to focus on the team getting the job done and we do not think it affects them."
As such, there will be more talks with the American and his representatives.
Edelman said: "We have a very good relationship with Stan and a continued dialogue with him, and will have to see how events unfold.
"We are joint-venture partners with them and expect to see them again in the near future.
"We have met Stan Kroenke. The chairman and I met him once in New York, I had met him previously in Denver, and we have a continued dialogue about Colorado Rapids, and we expect to see Stan regularly." Edelman added: "As far as Usmanov is concerned, we have always stated our belief as a responsible corporate body, we meet anybody who requests a meeting, and that is still our policy."
It would seem a logical step for Red and White Holdings Limited - now Arsenal's second-largest shareholder behind director Danny Fiszman - to seek a place on the board, which would possibly open the door for the return of former vice-chairman David Dein.
Edelman, however, stressed: "The board can review anybody being a director at any time, and either accept or decline it.
"If he had 49.999%, but the board did not think he would add value as a director, it would say no.
"It would have to go over 50% for the board not to have a choice."
Arsenal maintain their figures prove there is no need for them to seek the financial backing of an individual wealthy owner.
"We fundamentally believe the football club must be run for the long term from the cash resources which you drive out of the business," said Edelman.
"There is some kind of view that you need a wealthy benefactor to chuck lots of money at it.
"We fundamentally disagree with that logic.
"They may make an up front investment in the short term, but in the long run they are going to want to run it as a business and see a return on it.
"That is further complicated if the club is bought with debt and equity, because your debt financing has got to be serviced.
"You can put money in for a short period of time, but no-one is going to put money in for a year and a day."