Lukaku was unavailable for Solskjaer's first two games as interim boss either side of Christmas, handing the opportunity to Rashford, who then kept his place upon the Belgian's return.
Lukaku has come off the bench to score in both of United's last two Premier League games and netted when Rashford was rested in the FA Cup against Reading. But a report from the Daily Star claims that Solskjaer has decided the younger of the two will continue to lead the line.
It is alleged that the Norwegian coach has held talks with Rashford during the club's warm weather training camp in Dubai this week, making it 'clear' to the England star that he is the preferred choice over Lukaku in that central role.
The tabloid report even goes as far to claim that Rashford, who was often played out wide under the leadership of former manager Jose Mourinho, has been told it is 'his job to lose'.
Solskjaer recently spoke very highly of Rashford and his 'number nine' credentials.
"He gets kicked, he gets tackled, he goes for headers, he wins, he challenges, he runs. He is going to be a top, top number nine, definitely," the Old Trafford legend said of Rashford after the important Premier League win over Newcastle earlier this month.
The next opportunity for Rashford will come as United travel to Wembley to face Tottenham in what will be Solskjaer's first real test as manager after a favourable start. United were humiliated in the reverse fixture in Manchester in August but assistant coach Mike Phelan has insisted that the players are itching to get out onto the pitch and prove themselves.
"The players are really looking forward to it, you can tell that from just being around them. They understand that this is the stage that they want, they want to play in these huge games and they want to win these huge games," he is quoted as saying by the Daily Mirror.
"They want to be the best players on the football pitch again and we need to encourage that."