United also plan to invite the whole team as special guests to Sunday's FA Cup game against Tottenham at Old Trafford.
Havant chairman Marcus Hackney said: "United have been very kind in agreeing to let us use their training ground.
"As if it wasn't already a dream to be playing Liverpool, this just caps it all off."
United now use Carrington as their main training ground but The Cliff is still used by England when they meet up in the north or play at Old Trafford.
A club source also told The Sun: "It only took two phone calls and United immediate said 'Yes'.
"Perhaps they like the thought of helping the non-league minnows get one over on their biggest rivals."