The Red Devils host the Spanish champions at Old Trafford, in the first leg of their last-eight clash in Europe.
Rashford was forced to miss United's last outing against Wolves in the Premier League with an ankle injury, however, it is understood he trained with the senior squad during a morning session at the Aon complex.
The 21-year-old joined in with the first team after warming up alone as a precautionary measure and he is expected to play a part in the match against Barca.
Meanwhile, Bailly, Herrera and Matic were all missing as Solskjaer oversaw final preparations with his squad on Tuesday.
United have suffered an injury crisis over the last couple of months, which has coincided with a downturn in results on the pitch.
Solskjaer's men have lost three of their last four matches across all competitions and now face a real battle to qualify for next season's Champions League.
Bailly suffered a head injury while on international duty with Ivory Coast last month, while Herrera was ruled as unfit for the defeat to Wolves in the Premier League last week.
Matic was named on the bench at Molineux, but he has only just returned to the fold after missing Serbia's two fixtures during the international break.
The Red Devils are underdogs against Barcelona given their recent form, but a thrilling comeback victory in the round of 16 over Paris Saint-Germain will give supporters cause for optimism.
Before the second leg takes place at Camp Nou next week, United must negotiate a home game against West Ham in the Premier League.
Solskjaer will be desperate for a win to halt his side's current slide domestically, with three points currently separating them and fourth-placed Tottenham in the table with six matches of the campaign remaining.