The Gunners are top of the table and meet second-placed United at Old Trafford on Monday night in arguably the biggest game of the season so far.
Nani believes Arsene Wenger's young team have emerged as stronger challengers to United than champions Chelsea, who have struggled with injuries to key players and the loss of assistant boss Ray Wilkins.
The fear: Nani says Manchester United are more threatened by Arsenal - not Chelsea
They have slipped to third place after winning only one of their last six League games.
The Portugal winger's comments are even more controversial considering United play Chelsea at Stamford Bridge on Sunday week.
Nani said: 'Arsenal are a bigger threat than Chelsea now. Chelsea have lost a few games and drawn some and their confidence looks a bit low.
'But Arsenal have been winning, and being top gives you confidence. They are growing up in the way we are.'
Nani believes the return to form and fitness of players like Wayne Rooney and Anderson, who both impressed against Valencia on Tuesday, could not have come at a better time as United prepare for two huge games following the 7-1 win over Blackburn.
Perfect timing: Nani believes the return to form and fitness of Wayne Rooney has boosted United's hopes
He added: 'Our momentum is growing. Players like Wayne Rooney and Anderson are starting to play fantastically again. It's great because our next two games are going to be very important for us.
'If we win against Arsenal and Chelsea we will be in a very good position to win the League.'
United go into the game unbeaten in the League and with a game in hand over all their rivals.
Gunning for glory: Marouane Chamakh says Arsenal are capable of an upset at Old Trafford
But Arsenal striker Marouane Chamakh says they are confident of getting a result at Old Trafford after securing a place in the last 16 of the Champions League with a 3-1 win over Partizan Belgrade on Wednesday.
'Now we've reached the next round we can be 100 per cent focused on our match against Manchester United,' he said.
'It will be difficult, but we have had a good record in our away fixtures since the start of the season. I am confident. I know we can go up there and get a result.'
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