The 20-year-old is one of six frontmen at Sir Alex Ferguson's disposal at Old Trafford, having returned from a season-long loan stint at Sunderland last term.
Welbeck has hinted he is keen to break into the manager's first-team plans at United after spending most of his career so far out on loan.
But Ferguson has already indicated that he might struggle to keep his entire strike force happy, with last season's first-choice partnership Wayne Rooney and Javier Hernandez expected to put Dimitar Berbatov, Michael Owen, Federico Macheda and Welbeck in the shade.
The Trotters are reportedly poised to pounce for Welbeck if the manager chooses to send him out on loan again after he impressed at the Stadium of Light, scoring six goals.
But Bolton could face competition for Welbeck following speculation that Steve Bruce is keen to keep him with the Black Cats for another season.
Welbeck made a his United debut two months short of his 18th birthday and scored on both his Premier League and FA Cup debuts, then started the 2009 Carling Cup final win over Tottenham.
But that was arguably the high point of his Old Trafford career so far and he has not featured for his parent club for a year and a half.
Bolton boss Owen Coyle reaped the rewards of signing another youngster, Daniel Sturridge, on loan from Chelsea last season.
The 21-year-old was on target with eight goals in 12 appearances for the Premier League club and has also been linked with a return to the Reebok Stadium.