The Red Devils travel to Anfield on Sunday knowing that a victory would move them five points clear of Liverpool with eight games left to play.
United are currently fourth in the Premier League table but just a point behind third-placed Arsenal and two behind defending champions Manchester City.
And the 33-year-old Carrick feels that Louis van Gaal’s side have what it takes to finish above Liverpool in the table.
“Yeah, we have got to aim for that [second place],” Carrick said, speaking to United’s website after Sunday’s 3-0 win over Tottenham Hotspur.
“We’re within touching distance now. You look at the table and it is so tight. But I suppose really we’ve just got to look to the game on Sunday [Liverpool].
“There are going to be ups and downs because that is how it is, especially in the last nine or 10 games. Sunday is a big game for a lot of reasons and that is probably all we can focus on at the moment.”
Liverpool kept pace with their top-four chasing rivals thanks to a 1-0 win at Swansea City on Monday night.
United still have to face local rivals Manchester City, leaders Chelsea, Everton and Arsenal before the end of Van Gaal’s first season in charge at Old Trafford.
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