Wilshere, Sanchez and Ozil will all be out of contract this summer, but while Sanchez and Ozil are expected to leave, Wilshere is said to be close to signing a new deal at the club.
The England midfielder struggled during a loan spell at Bournemouth last season, but has worked his way back into the fold in recent weeks, and scored against Chelsea in the Premier League on Wednesday night.
Keown has branded Wilshere "a force to be reckoned with", and the former centre-back is confident that the 26-year-old will soon sign a new contract with the Gunners.
"Jack proved against Chelsea on Wednesday that he is well and truly back, and a force to be reckoned with," Keown told the Daily Mail.
"He is a superstar approaching the levels of Alexis Sanchez and Mesut Ozil but, crucially, he wants to play for Arsenal. The uncertainty surrounding the futures of Sanchez and Ozil has created a flat feeling at Arsenal.
"Wilshere is the figurehead in this dressing room and does not take any nonsense. He has taken those fighting qualities which have seen him battle back from injury and is displaying them to great effect. He is the dynamo in Arsenal's engine room.
"It should be a formality that he signs a new contract. Given his injury history, he will have to be realistic and the club may want to build something into his deal which is linked to appearances. If Wilshere plays, he should be paid top dollar, but allowances have to be made for if he has another lengthy injury lay-off."
Wilshere has already made 19 appearances in all competitions for Arsenal this season.