The England man was ruled out of the side's last two games while the Mexican picked up a knock at Stoke. In defence, Nemanja Vidic is tipped to return against Liverpool
Rooney was unable to play in United’s 1-1 draw with Stoke last Saturday while Chicharito was forced to leave the pitch after picking up a dead leg less than five minutes into the game.
"Wayne and Hernandez are fit for tomorrow. They trained very well yesterday, which is pleasing," Sir Alex told reporters.
United have had a number of injury problems this season, with the loss of centre-backs Jonny Evans and Nemanja Vidic, makeshift right-back Chris Smalling, and rising starlet Tom Cleverley.
But the manager is hopeful of their return in the near future, adding: "We'll hopefully have Jonny Evans back too. At the moment we're making too many changes in the back four so hopefully his return will help us with the defensive part.
"Vidic, Cleverley and Smalling should be ready after the internationals and available for Liverpool."
United were criticised after their dismal performance against Basel on Tuesday, in which their opponents scored three goals after capitalising on a soft defence.
United gave up a 2-0 lead in the first half as it looked like they were cruising to yet another victory, but they allowed Basel to take the lead in the second, and only managed to come away from the game with a point after Ashley Young’s late equaliser.
"People will say our performance was careless against Basel and that we underestimated our opponents," Sir Alec continued.
"I think there's an element of truth in that and we have to do better defensively. We are too cavalier at the moment."