Nani has stolen a march on United's three other summer imports.
But Reds' boss Sir Alex Ferguson expects Carlos Tevez, Owen Hargreaves and Anderson to catch up as the campaign moves on.
Portuguese winger Nani was the only newcomer who was able to play on United's pre- season tour of the Far East and take part fully in the champions' pre-season training programme. It has given the 20-year-old a head start.
"Any player who comes into the English game finds it difficult if they haven't done a pre-season," said the United boss.
"If they miss the pre-season it is very difficult. The one who is well ahead on fitness is Nani.
"He is looking much, much better."
Tevez returned to Carrington on Wednesday after playing for Argentina in Australia and Fergie is now expecting the striker to make more progress.
"Carlos missed our pre- season because of Copa America and the way the transfer dragged on," Sir Alex added.
"Then unfortunately the way fixtures have panned out, we have not had a lot of time to work on him. But the games are helping him."
Anderson had a disappointing debut against Sunderland before being taken off at half-time but Fergie believes the international break came at a good time for the Brazilian.
"Anderson did not go away with Brazil so more work has been done with him at Carrington. It will help him."
Ferguson wants Gary Neville, who has been injured since March, to get minutes under his belt before promoting him back to first-team status.
"He needs a couple of reserve games." added Fergie. "He did well in a practice game."