The Glazer family said in November that they had began exploring options for the 20-times English champions, including new investment or a possible full sale of the club.
"We have formally put ourselves into the process," a spokesperson for INEOS told the Times newspaper.
Ratcliffe, a long-time fan, expressed interest in buying the club in August, as reported by Reuters.
Bids are expected to come from the Middle East, US and Asia for Man Utd, but the British billionaire is the first to express his interest publicly.
Interested parties have to speak with the merchant bank running the sale on behalf of the Glazers.
United fans have been clamouring for changes, and the ownership has been the target of intense criticism as the team last won silverware in 2017.
The Red Devils are currently fourth in the Premier League on 38 points, one point behind local rivals Manchester City but nine adrift of leaders Arsenal.
