The Daily Mail says Solskjaer has noticed a worrying change in Rashford's behaviour amid talk he could leave for Barcelona.
Rashford is demanding wages in the region of £200,000-a-week in order to commit his long-term future to United.
And Solskjaer has been left concerned by his star striker.
It is claimed the 46-year-old believes the youngster to be uncharacteristically sulky, cutting a frustrated figure at times on the pitch.
Solskjaer supposedly believes that Rashford has shown a tendency to sulk when the tide of a game is not going his way.