Arsenal had intially expected Welbeck to return in February.
Welbeck was initially due to return in the new year
The former Manchester United star suffered a serious knee injury towards the end of last season, with initial reports suggesting he was unlikely to play again in 2016, with February 2017 touted as a potential return date.
However, ahead of his side's trip to Premier League champions Leicester City this weekend, Wenger reportedly told reporters that Welbeck could be poised to return before the turn of the year.
According to The Independent, he said: “He has an inflammation of his knee and they had to go in again to see if it is healing well or not.
“If the healing was not good, he would have been out until April, but the news was excellent and he will be back around Christmas.
“He had a second check with a camera inside. That was the good news of last week, the only good news. That was very positive.”
The England international has seen his career at the Emirates plagued by injuries since his arrival from Old Trafford, with his latest spell on the sidelines coming just three months after a 10-month lay-off.
The news of Welbeck's progress is likely to be warmly welcomed by Wenger, who after a 4-3 defeat at home to Liverpool on the opening day has found himself under increased pressure from the club's fans.
His side travel to the King Power Stadium without eight first-team members, with both Aaron Ramsey and Alex Iwobi among the most notable names on his injury list.