The Uruguayan was impressive in his United debut against Derby County on Sunday, scoring in the 2-1 victory.
Pellistri spent the second half of last season on loan at Alaves, and Solskjaer has revealed clubs are clamouring for his signature.
"I thought he was bright and he took his goal really well," Solskjaer said. "Great first touch. Good pass by Shola [Shoretire] but great first touch with sets him up.
"It was a very good goal, the first touch set him up and he's very good at dribbling so going past the goalkeeper wasn't a problem. He was bright when he came on.
"I think he showed what he is because he's a difficult player to play against. One against one he can go past people so very pleased with him.
"I can see a loan deal for him, there's been loads of interest and for his best interests a loan would be what we look for."