The Red Devils currently enjoy a seven-point lead at the top of the Premier League, and will face Real Madrid in the pick of the ties in the last 16 in Europe's top club competition.
“Yeah, everything is possible,” Evra told reprters when asked if United could win the treble.
“If Manchester United win the Champions League, the Premier League and the FA Cup, I’ll say it’s the best team I’ve ever played in, because I’ve only ever won two trophies in a season before.
“We’ll see at the end of the season. But I don’t want to start to talk about targets. I just want to concentrate on each game, winning each game and improving as a team in each game.
“And after that, we’re going to be difficult to beat.”
|CHAMPIONS LEAGUE LATEST
|14/1||Manchester United are 14/1 with Bet365 to win the Champions League
“That team was unbelievable,” said Evra. “When I went back to France and people were asking ‘What has happened to your team? You’re running everywhere, you’re scoring a lot of goals, you have players like Carlos Tevez and Cristiano Ronaldo.’
“It was a strong team, so it’s difficult to compare. If we win the Champions League and the league, we can compare the teams but in the end we have to win something.
“We’ve got more experience - Robin van Persie has come into the team and the younger players, such as Tom Cleverley, are getting more mature.
“We don’t want what happened last year to happen again. We’re focused on winning the league - because we’re Manchester United. No-one thought that would happen last year. We were all really, really disappointed.
“I remember people were saying we didn’t play great football, but in the end we finished on level points with City. That’s why I said that if we play well this season, I think we can win the title.
“I’m really confident this year, because we’ve won against City, we’ve won against Chelsea, we’ve won against Arsenal, now we’ve beaten Liverpool twice. For our confidence, you couldn’t get much better.”
The Frenchman also hailed his side's solidity in defence as being crucial to their bid for trophies, and praised his team-mates' willingness and determination to defend from the front.
“It’s really important if you want to win the title,” said Evra. "You have to win the title with a strong team and a strong defence, but I don’t only like to talk about the four defenders and the goalkeeper when you concede goals. It’s about the team.
“If you look at the performance against Liverpool, someone like Danny Welbeck ran more than anyone on the pitch and he’s a striker. That makes the difference.
“It’s not just about the defence, it’s about everyone, and when Manchester United play with that spirit, this is the United spirit.
“When you first come here, that is one of the first things Sir Alex Ferguson tells you - 'You’re here to work, not for a holiday or something.”