According to Sky Sports,Oxlade-Chamberlain will hold talks over his future at Arsenal later this week.
Arsenal manager Arsene Wenger said last week that he hoped the player would extend his current contract, which only has one year left on it, and he will meet with Oxlade-Chamberlain, along with chief executive Ivan Gazidis to discuss the player's future.
The 24-year-old England international has attracted interest from Premier League rivals Liverpool, Manchester City and Chelsea, but Winterburn believes it is essential that the club keep hold of him after he has excelled in his new role.
"I absolutely say he's a player that has made massive strides in the last season," Winterburn said. "At wing-back, I would put him as Arsenal's outstanding player.
"From the end of last season through to the start of this season I rate him that highly. Is that a position that he wants to play regularly though? Does he want to play in centre midfield or a more advanced area in behind a main striker?
"Then it comes down to the amount of money that he's being offered, does he feel he's been offered less than some of the other players in the team but he feels as important as them?"
Winterburn added: "He's had a slight problem in that when he looks like he's going to establish himself into the team, he's picked up an injury, had several weeks out, come back in and picked up another injury.
"But from the end of last season his performances have been at a very high level. He's definitely a player Arsenal need to keep."