The Red Devils were offered Bale on loan by Real Madrid.
But now he looks set to sign for Tottenham instead.
Per the London Evening Standard, Solskjaer worried about Bale's injury record in the past few years.
He has not played very much for Real Madrid, and looked poor for Wales during the recent international break.
Bale would be on high wages, even if Real paid some of his salary, and Solskjaer does not want a player who has such fitness doubts surrounding him.