Wilshere appeared in footage obtained by the Daily Mirror that is said to show him in the wake of the bust-up on Sunday morning.
In the footage a number of police officers can be seen as a group of people, said to be his friends, attempt to obscure him from the view of onlookers filming the star on their mobile phones.
His club told The Sun that the midfielder denied any involvement in the earlier incident and described it as a "private matter".
According to the newspaper Wilshere had earlier been at the Cafe de Paris nightclub near Leicester Square.
The nightclub told the newspaper that a "Jack" was asked to leave before adding: "He is welcome back any time."
There were conflicting newspaper reports of what time the incident occurred.
A Scotland Yard spokesman said: "At 2.15am on 3 April, police patrolling Coventry Street became aware of two groups of males involved in an altercation.
"Officers intervened and one man claimed he was assaulted. He did not require hospital treatment.
"There have been no arrests and inquiries continue. We will not comment on who may or may not have been involved."