Solskjaer is keen to sign a fast centre-back to play alongside captain, Harry Maguire next season, as that will enable him to play a higher line.
The Norwegian is targeting Bournemouth star, Nathan Ake but they face competition from Premier League rivals Manchester City for his signature.
But Solskjaer, who has already held talks with the club’s executive vice-chairman, Ed Woodward, made it clear that Smalling will not return to Old Trafford if the Red Devils sign a top centre-back.
Smalling is currently on loan at Serie A side, AS Roma.
The England star joined the Italian club following the £80million arrival of Maguire from Leicester last summer.
The 30-year-old originally signed a one-year loan, expiring in June, but following the COVID-19 break, Smalling had his stint in Italy extended until the first week of August in order to be able to play out the end of the Serie A season.
