Erik ten Hag's side take on the Cherries at the Vitality Stadium on Saturday, looking to keep their top four hopes alive.
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Rashford had missed his side's 2-0 victory over Wolves with a leg injury.
His speedy recovery is certainly a welcome boost for the Red Devils, as they look to clinch Champions League football for next season.
Ten Hag's troops need two wins from their last three matches to secure a place in Europe's elite competition.
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The 25-year-old is Man United's top scorer this campaign with 16 goals to his name so far.
With three days before United head to the south coast, Rashford is expected to be fit and could feature.
Ten Hag will provide an indication of his current situation when he faces the media on Friday.
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Marcel Sabitzer has been ruled out for the campaign, along with fellow teammates Lisandro Martinez and Donny van de Beek.
The trio will, therefore, miss the FA Cup final on June 3 when United go toe-to-toe with Man City at Wembley.
Ten Hag's side are currently fourth in the Premier League with 66 points, one points ahead of fifth-placed Liverpool, with a game in hand.