Lingard and Rashford are two of the biggest stars at Manchester United, with the former launching his own fashion label last year.
The Sun claim Mike Phelan and Solskjaer have spoken to the attacking duo about putting their football first.
Uniteds narrow win over Leicester City on Saturday eased the pressure on Solskjaer, but the coach was concerned with Lingards commitments outside of football.
With assistant coach Phelan backing him up, Solskjaer warned Lingard to put work on his brand on the backburner while he focused on improving.
Rashford was given the same warning as Solskjaer feared he could be similarly distracted.
Solskjaer has turned to Rashford to lead his line after an injury to Anthony Martial and the Norwegian has shown in the past he rates the Englishman as his No.1 striker.
After a difficult spell of form before the international break, Rashford and United responded with a hard-fought victory over Leicester.
Rashford scoring an early penalty, which proved to be the difference between the two sides at Old Trafford.
Lingard missed the visit of Leicester after withdrawing from international duty with England due to illness.
Solskjaer urged Rashford to score more goals before he produced the goods against the Foxes.
You have 38 [league] games, so if you can have 19 goals [each] as a partnership, with those two, so around 40 goals, thats OK, but its not top, top class, said Solskjaer before the game against Leicester.