The England worldwide has yet to make a single appearance for the Gunners this season, having broken his ankle during the summer and then being hit with a series of setbacks.
“I will be cautious, I would say four weeks”.
Wenger had said on Friday that it usually takes six weeks to recover full fitness after starting to run again but he clearly hopes that the timescale will be reduced.
“He is looking quite good and overall, I had a short chat with Roy Hodgson about him and reassured him that Wilshere is progressing well”, Wenger told reporters at a news conference.
Rosicky played his first game of the season against Burnley in the FA Cup during the weekend by coming on as a substitute in a 2-1 victory, but the Czech Republic worldwide picked up a thigh problem and is expected to be out for another six weeks.
Wenger said: “Santi is still not outside”.
“Loyalty works two ways”.
Wenger believes the player has shown more than enough in his time with Chelsea to suggest he has a bright future on and off the field.
On transfers, Wenger said it was highly unlikely there would be any more at the North London club after the club signed Egyptian midfielder Mohamed Elneny from Swiss side FC Basel earlier this month. That’s never a coincidence. When you lose players like that you’re always in danger.
“100 per cent is hard to say, but 99 per cent sure, yes”, he said of any deadline day recruitment.
There could yet be a couple of temporary departures as Wenger is hopeful of loaning out both Serge Gnabry and Mathieu Debuchy before the window closes on Monday evening.