The England international, who has scored a career-high 28 goals this season, suffered a groin strain in a 2-0 win over Everton on April 8th.
United said last week that Rashford would likely be absent for a "few games" but he could make a timely return in Spain, with Erik ten Hag's men in the hunt for a treble of cup competitions.
The tie is finely balanced at 2-2 after two late own goals conceded by United in the first leg at Old Trafford.
Luke Shaw and Marcel Sabitzer also took part in training on Wednesday to ease the Red Devils' injury crisis.
First-choice centre-backs Lisandro Martinez and Raphael Varane are unavailable after picking up injuries in the first leg.
Bruno Fernandes is suspended, while Donny van de Beek and Alejandro Garnacho also remain sidelined by injury.
United, who lifted the League Cup earlier this season to end a six-year trophy drought, face Brighton on Sunday in the FA Cup semi-finals.
