Ibrahimovic said this week he believes he is still capable of performing in the Premier League adding that "if United needs me, I'm here."
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The former Sweden international scored 29 goals in 53 appearances at Old Trafford between 2016 and 2018 and Solskjaer appeared to leave the door open when asked about a possible move for the 37-year-old.
"If he was 28 and not 38 [in October], there's a big difference," Solskjaer told a news conference on Friday. "Zlatan had a great time here, he's still doing well, it's unfortunate he got his injury here.
"Who knows, he knows my number, he looked at my house [when he was here]. We can speak a native language. If he's serious I'll always speak to Zlatan.
"I don't think that will happen, I think he's had his time at the club, he's had a fantastic career at the club."
Solskjaer has seen his attacking options reduced this summer after the departures ofRomelu Lukakuand Alexis Sanchez to Inter Milan.
It leaves the Norwegian with just Marcus Rashford, Anthony Martial and 17-year-old Mason Greenwood as the only recognised centre forwards in the squad. Martial is set to miss the trip to Southampton on Saturday because of a thigh injury but Solskjaer is insistent it was the right decision to let Sanchez leave.
"Alexis needed to go," Solskjaer said. "He's been here for 18 months and it's not really worked out for him.
"For him to restart and get himself playing regularly and scoring goals that will only benefit everyone in the end. He will come good for them. For us we had a decision to make. I'm trusting Anthony, Marcus, Mason to be our centre forwards.
"We've got wingers in Chongy [Tahith Chong], Dan James, [Andreas] Pereira. We've got loads of options. For me it's time for our boys to feel that pressure and responsibility, to be more robust, to know they have to play five games in a row."
Chris Smalling has signed for Roma on loan and Solskjaer added thatMatteo Darmian could also leave before Monday's deadline, with Parma close to sealing a deal for the Italy right-back, according to ESPN FC sources.
Smalling flew to Italy on Friday morning to finalise a season-long deal with the Serie A side. Darmian is also set to return to Italy but Marcos Rojo will stay at Old Trafford despite interest from AC Milan, Monaco and Marseille.
"The opportunity for Chris is something that came up the last couple of days," Solskjaer told a news conference on Friday. "We sat down [on Thursday] and I couldn't promise Chris regular football.
"It's a big club and hopefully he will come back stronger for it. There is some interest in Matteo from Italy and he wants to go back home. Marcos is definitely staying.
"The squad is now less in numbers but it's big enough and strong enough to have cover in all positions."
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