The former United midfield star recently left his position in charge of Oldham, citing differences with the owners.
Solskjaer would be happy to welcome Scholes to Carrington, whether it is for a chat or a deeper role.
Speaking about Scholes during his press conference, Solskjaer said: "He's probably got his reasons why he has left.
"I've texted him.
"You have to ask him [what happened]. He is invited here if he wants to come and have a chat about it."