Former United manager Jose Mourinho described Rashford is “a man of movement”, and not a “pure No 9”.
But Solskjaer maintains there are “different ways of playing with Marcus”.
“I think since Anthony [Martial] has come back, Marcus has flourished,” said Solskjaer.
“He’s probably happier facing goal, being direct, driving at people, taking players on instead of being that target man – back to goal.
“Marcus wants to master all the skills in the end, he’s only 22.
“So I’m sure we’ll see him up front as a 9, maybe as a two with Anthony, maybe as a three like we did against Norwich or wide like we did against Chelsea.”
United had made their worst start to a Premier League season in 30 years after seven league matches, but a draw against leaders Liverpool has been followed by victory over Norwich as well as cup wins over Chelsea and Partizan Belgrade.
Another win over Bournemouth could take United back into the top six.
