Ronaldo, 36, looks set to leave Juventus after telling the club he wants to move before the Aug. 31 deadline and asked about a return to Old Trafford. Solskjaer refused to categorically rule out a move for Ronaldo, who has been heavily linked with Manchester City.
"I didn't think Cristiano would leave Juventus," Solskjaer told a news conference on Friday. "If he ever wants to move away from Juventus he knows we are here.
"For me he is the greatest player of all time. We have had a bit of communication and I know Bruno [Fernandes] has been talking to him as well. There's been a lot of speculation the last few days.
"Let's see what happens with Cristiano, he's a legend of this club. I played with him and coached him. He's a tremendous human being. Let's see what happens with Cristiano."
Meanwhile, City boss Pep Guardiola said he believes it is unlikely Ronaldo will move to the Etihad Stadium before Tuesday's transfer deadline.
Speaking on Friday, Juventus manager Massimiliano Allegri revealed Ronaldo has asked to leave the club, but Guardiola does not believe he will get a new striker before Tuesday's transfer deadline.
"I cannot say much so Harry Kane announces continuing at his club, as exceptional club like Tottenham and Cristiano was a Juventus player, I think is a Juventus player and I cannot add anything else," Guardiola told a news conference.
"Only I can say I think there is three or four days left and anything can happen, but in my personal view there are few players, Ronaldo is included and [Lionel] Messi, they decide where they are going to play.
"They lead in the negotiations and right now that is my feeling. I am more delighted with the squad I have and we will stay the same. All I can say is we are incredibly fortunate to see and enjoy the best two players in the last 20-30 years.
"The Argentinian and Portuguese guys were amazing in every club. I don't think we will watch anything quite similar in the future. I am incredibly happy with the squad I have, more than satisfied. We are the same squad except one player leaves Sergio and we have Jack.
"Messi decides himself where he wants to play. He decides to go to Paris. These players decide. They know the door. After that there are situations I cannot control as it is not my business."