The arrival of Vladimir Labant is likely to threaten his place in the line-up, but Winterburn reveals it is old father time catching up on him that is the main factor behind his decision.
Labant sealed his move from Sparta Prague for £900,000, on a two-and-a-half year contract on Friday.
"I have spoken to Glenn and I understand the situation, which is really quite clear. I am 38, playing in The Premiership and delighted with that," Winterburn told the club's official website.
"But my time is moving towards its end and I think Glenn felt that he needed to bring someone in to fill that position.
"I'm 90 percent certain that I'll be leaving at the end of the season, but while I'm at the club hopefully I can hold that position down.
"I'd love to stay and play for another season, but I'm not sure whether at this stage it is realistic, so I think it is fair that I should just concentrate for the rest of this season and hopefully I'll be in the team and then we will look at the situation from there."
The former Gunners full back has yet to decide whether he will continue playing at a lower level, or to hang up his boots instead.
He will wait until the end of the campaign before settling on his future plans, but he says it is the recovery period after matches that is affecting him at present.
"I'm feeling okay during the game at the moment, but after the game I'm absolutely shattered," said Winterburn.
"That is the main difference when you get to my age. It is not the games, but the recovery after, and we have just had five games in two weeks, which has near enough wiped me out.
"I want to still do myself justice and don't want to take it too far, but I want to give it everything for the rest of the season, and then whatever happens at the end of it, will happen."