The Sun says United chiefs want to keep fighting for the title and qualify for the Champions League before Solskjaer is offered a new deal.
The Norwegian has just 16 months left and SunSport understands United could hand him another two-year deal.
They are willing to give Solskjaer, 47, an increase in wages, taking his annual salary to around £6million before bonuses.
But his team have been inconsistent, including a shock recent home loss to Sheffield United.
And on top of their Champions League group stage exit, concerns have been raised.