The Londoners have a one-point lead over United but have played a game more than them and Frenchman Evra said champions Chelsea, a further point behind in third, were his club's biggest title rivals despite their recent shaky form.
"For me, (Arsenal) is a football training centre. I watch their match, I enjoy it, but are you going to win a title afterwards?" Evra said on French television channel Canal Plus.
"Our real enemy is Chelsea. They can win the title. We are more attentive to Chelsea's results than Arsenal's."
Since winning the FA Cup in 2005, Arsene Wenger's men have failed to win another trophy although they have played an attractive brand of football.
"I hear them being compared to Barcelona. Barca play beautiful football but they win," said Evra.
"In 20 years, people are not going to remember Arsenal's football. People remember trophies. We can lose against them on the 13th (Monday) but at the end of the day, there is nothing, no trophy, nothing.
"Arsenal is a big club that has not won anything in five years: that is a crisis."
Wenger refused to get drawn into a war of words, saying his policy was always to respect opponents.
"We are guided by the way we want to play football and not by the statements of anybody who plays against us," the Frenchman told a news conference.
"Personally, I believe you always respect your opponent and that is what we try to do. We don't want to go into any unneeded talking before the game and we want to focus on the way we want to perform and play and ignore any provocation before a game."
It is not the first time Evra has mocked the Londoners. In 2009, the Frenchman described a Champions League tie as "11 men against 11 children" when United beat Arsenal 3-1 at the Emirates stadium and knocked them out of Europe.
Not everyone at United agrees with Evra, though, with Portugal winger Nani saying Arsenal pose a bigger threat than Chelsea, who have won just two of their last eight games in all competitions.
"Chelsea have lost a few games and drawn some and their confidence looks a bit low," British media quoted Nani as saying. "But Arsenal have been winning and being top of the league gives you great confidence."
