The One Direction star, who bears a striking resemblance to Mick, 68, will reportedly fly to the US to try out for the lead role in Exile On Main St, which is named after the band's hit 1972 album.
'Harry on stage can pass as a dead ringer for Jagger,' says a source.
'If he can transform this image into a movie role then he's going to be a serious candidate to get the part. The signs are so far good.'
Harry, 18, first tried his hand at acting during One Direction's guest appearance on US Nickelodeon show iCarly earlier this year.
If he begins a film career he's likely to triple his earnings but there are worries that he'll be unable to fit his 1D commitments around shooting.
'The film is going to be a lot of work and very demanding,' the source tells The People.
'If Harry takes the part it will lead to concerns about his involvement with One Direction.
'The band is his main priority but it is flattering to have so much interest from such senior people in the film industry - he couldn't miss this opportunity.'