The 21-year-old has been in sublime form since the Norwegians arrival at Old Trafford with three goals in his last five appearances.
One of Solskjaers key changes since taking over from Jose Mourinho at United has been to play Rashford as a central striker instead of out wide.
And according to the Daily Star, Rashford has been told by Solskjaer during Uniteds warm-weather training camp in Dubai this week that he is now considered as the No.1 striker ahead of Lukaku.
The report also claims that Rashford will start ahead of Lukaku for Uniteds clash with Tottenham at Wembley on Sunday.
Lukaku missed Solskjaers first two games in charge after being granted compassionate leave but has scored in all three of the games he has played since returning.
Solskjaer has won all five of his games in charge so far and Uniteds first-team coach Kieran McKenna has praised the 45-year-olds impact.
I think that, whether the players are 17 or 18 or senior internationals or top, top players, I think they want the same things.
They want to be treated with respect and they want you to help them with their game and improve them as individuals, when the time is right.
If you give them those things, you get a really good response from them. I have to say the players have been first class, with their attitude and willingness to learn. They are a really good bunch to work with and that has helped, of course.
The staff around the team have also been a great help and Im looking forward to kicking on now and a positive few years for the club.
Over the last couple of weeks, Ole and Mike [Phelan] are coming in with different experiences and different skill sets so the chemistry and dynamic is really good at the moment. Theyre enjoyable staff to work with.
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