The tickets only went on sale on Monday and the early sales indicate the huge affection still held at Old Trafford for Keane despite his shock departure from the club in November.
Celtic have been allocated the entire 25,500-capacity North Stand for the game and are confident they will fill it.
The match, part of Keane's severance from United, is likely to net the former Republic of Ireland captain in excess of £2.5million in gate receipts, although it is believed Keane will donate the money to charity.
The 34-year-old has already indicated his intention to give 1,000 tickets away to local school children and United supporters' club branches.