The Gunners star suffered an ankle problem during Arsenal’s 0-0 draw with Sporting Lisbon earlier this month to curtail what had been an encouraging start to the Premier League season.
Welbeck underwent ankle surgery last week to start the rehabilitation process but Arsenal have since confirmed the 27-year-old will require a second operation.
The former Sunderland striker has entered the final 12 months of his current deal to leave both the club and player in an awkward position after his injury setback.
But former Arsenal striker Wright believes the Gunners should give the England international at least another 12 months to prove his fitness and sharpness when he returns from injury.
“I would keep him,” Wright told BBC Radio 5 Live last Monday night.
“I’d sign him for another year. Get him fit and see where he is.
“He is a fantastic professional and he never lets Arsenal down.”
Welbeck has been forced to sit out 83 games due to injury since the England striker moved to Arsenal in a £16m deal from Manchester United in the 2014 summer transfer window.
That translates to 587 days on the sidelines through fitness problems, earning Welbeck the unwanted tag of being injury prone.
Arsenal will return to Premier League action on Sunday with a trip to Bournemouth when the Gunners look to end a run of three successive draws in the top flight.
The Gunners are in fifth place in the Premier League and three points behind derby rivals Tottenham Hotspur, who occupy the final Champions League spot.
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