Raiola said last week he and Pogba would decide whether the World Cup winner will remain at Old Trafford at the end of the season, having stated the midfielder would be open to a return to Juventus.
Solskjaer responded by saying he was sure the 26-year-old, who has been sidelined by an ankle injury since December, still wanted to play for United. He added: "Paul is our player, not Mino's."
Raiola hit back at the Red Devils manager on social media, suggesting he focus his attention elsewhere amid reports United are lining up potential replacements as manager.
"Paul is not mine and for sure not Solskjaer's property, Paul is Paul Pogba's. You cannot own a human being already for a long time in the UK or anywhere else. I HOPE Solskjaer DO NOT WANT TO SUGGEST THAT PAUL IS HIS PRISONER," Raiola wrote.
"BUT BEFORE Solskjaer makes comments about things I say he should inform himself better about the content of what has been said.
"I am a free citizen who can think and express my thoughts. Until now I was maybe to [sic] nice to him. Solskjaer should just remember things that he said in the summer to Paul.
"I think Solskjaer may be frustrated for different reasons and is now mixing up some issues.
"I think that Solskjaer has other things to worry about. AT LEAST IF I WAS HIM I WOULD."