Arsene Wenger believes Jack Wilshere could make his recovery from a hairline fracture to his left fibula within three to four weeks.
The England midfielder picked up the injury in a collision in training, and the initial prognosis was that he would miss "several weeks".
It is the latest in a long line of problems for Wilshere, who has been plagued by fitness concerns over the past few years.
But in a media conference on Friday, Wenger said: "Jack is back in training but I thought at the start it will be six to eight weeks but it could be three to four so that is positive news.
"I always bring him back when he says he is ready and when the fitness coaches say he has the quantity of work behind.
"You come back to the relationship with your fitness and medical people that is confirmed by what I see in training.
"Maybe when he was younger we overplayed him because he was such a good player but now we are cautious with him."
Wenger also confirmed that Alexis Sanchez is fit and ready to play at Crystal Palace on Sunday after a substitute's appearance against West Ham last weekend, but Danny Welbeck's knee problem will see him sidelined until at least September.
"Alexis is fit and did good work during the week and is available for selection," Wenger added.
"Compared to last week's game we haven't lost anybody. [Hector] Bellerin is back available again and other injuries like Welbeck, Wilshere are not back.
"Welbeck is not close because he has not started full training so I would say at least three weeks from today."
Last weekend's 2-0 defeat to West Ham led some to suggest Wenger needs to further add to his squad before the transfer window closes, but for now the Frenchman is focusing on bouncing back in Sunday's trip to Crystal Palace.
"We were as open before that result as after," he said. "We are working hard and focused on what can strengthen our squad.
"The availability is not big. Now it is important we focus on our game on Sunday."
