The Harry Potter actor has recently taken part in a workshop reading of the play with director Ian Rickson, with a cast that also included Daniel Mays and Robert Sheehan.
Butterworth's play, which was originally directed by Rickson at the Royal Court starring Tom Hollander, Aidan Gillen and Andy Serkis, is set in a 1950's Soho club and follows a rock singer with star potential who gets caught up in the seedy underworld of the club.
Grint, who is best known for playing Ron Weasley in the Harry Potter series alongside Daniel Radcliffe and Emma Watson, told the Telegraph this week that he is "seriously considering a new West End role", and it seems that Mojo could be the one.
Rickson, who has had successes with other Butterworth plays including Jerusalem and The River, and producer Sonia Friedman are said to be in negotiations with Grint and Whishaw according the Mail's Baz Bamigboye. The production could be seen in the West End next year.