The striker has not featured for the north London club this season after undergoing knee surgery last year but is edging closer towards full fitness.
Welbeck has been training with Arsenal’s first team in recent days as he steps up his rehabilitation.
And Wenger has revealed that Welbeck could feature against Brighton and Hove Albion’s second string at the club’s London Colney training base on Friday.
Writing in his Arsenal programme notes before the Gunners’ goalless draw against Southampton on Tuesday night, Wenger said: “Danny Welbeck is stepping up his rehabilitation.
“We have to remember that he has not played since April 2015 and will need a game with the Under-21s, where we can monitor him and leave him free to play at his level of commitment. That looks to be very soon, maybe this week.”
Welbeck scored eight goals in his first 34 games for Arsenal after joining the north London club from rivals Manchester United last summer.
His last appearance for the club came in the 2-1 win over Reading back on 18 April.
Arsenal, who are fourth in the Premier League table, travel to Bournemouth on Sunday lunchtime.
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