A man who left Camp Nou for Arsenal in 2014 has been nursing knee ligament damage of late.
He has not figured for the Red Devils since March 2, with an untimely injury forcing him back onto the sidelines during an ongoing struggle for form.
United are yet to see the best of a forward with just two goals to his name this season but are preparing to offer him another clean slate.
Solskjaer is not expecting the 30-year-old to figure in a Premier League clash with West Ham on Saturday but is hoping to have him back for European duty on Tuesday.
The Red Devils boss said when asked for an update on the South American: “He is training with us.
“He's trained twice, trained today, I'm not sure if he's going be available [for West Ham].
“He's injury-free but not sure 100 per cent for tomorrow, maybe more likely for the Barcelona game. Let's see.”
Solskjaer has plenty of other attacking options at his disposal for a home date with West Ham.
He is, however, looking to continue with a rotation policy that allows him to keep key men fresh at a crucial stage of the season.
“I've still got options of course to rest one or two because there are games coming up and they'll all play a part,” said Solskjaer.
“We had players on the bench on Wednesday night like Jess [Lingard] and Anthony [Martial] who normally start games.
“There will be a couple of changes. Let's see what we'll decide on.”
While planning to shuffle his pack once more, Solskjaer has a number of players unavailable to him.
“[Ander Herrera is] still out, won't be available,” he added.
“I doubt Nemanja [Matic] is available because of his illness, maybe because he's a warrior and wants to join in and help his team-mates [he'll play].
“Let’s see after today. He trained individually yesterday.
“We've got a couple of other full-backs out for a while.
“Matteo [Darmian] will be available, [Marcos] Rojo's available and we might just have to look at other options as well.”
United will head into a meeting with the Hammers sat sixth in the Premier League table, three points adrift of the Champions League spots.
They will be hoping to get the likes of Sanchez and Matic back into their plans as quickly as possible, as the big games are coming thick and fast at home and abroad.