The French full-back, who has also been struggling with a knee problem, was withdrawn in the second half of Saturday's comprehensive 4-0 victory over the Magpies but is hopeful he can make the starting XI at the Allianz Arena.
"I think I will be fit," Evra told the club's official website. "I received a knock and I was injured as well before Aston Villa with my knee so I will try my best to be fit.
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Evra missed the first leg against Bayern through suspension but is now eagerly awaiting the away leg as United bid to "surprise everyone", while he also praised Alexander Buttner for coping so well in his absence.
"I was really frustrated to not play in such a big game [the first leg] but I though Alex did a good job," the defender continued.
"I was so pleased with the performance of the lads and now we must make sure we pull off a shock because Bayern are favourites for this game.
"It is not often since I have played for Manchester United that we are not the favourites but, sometimes, you have to accept they are favourites and let’s surprise everyone."
Evra also admitted he has seen parallels between United's lacklustre season and Chelsea's Champions League-winning campaign two years ago, with both sides struggling domestically but flourishing in Europe.
"It was funny because all season reminded me of the Chelsea season [when they won the Champions League in 2012] when they were not playing well in the league," he added.
"I keep this in my mind. I am not saying we are going to do the same but sometimes you have to be positive so why not? You have to believe."