Real were boosted by a 4-1 demolition of Sevilla in which the in-form Cristiano Ronaldo scored a hat-trick.
It was a stark contrast from the game against Granada which saw Real slip to their only defeat of the season last weekend.
Initially, Jose Mourinho made complaints that the scheduling of the game worked against the Spaniards, but United had to face Everton on the Sunday so Real have had an extra day's rest.
"Real Madrid are coming into the match in good form, and not because of (last night's) result," Karanka told Sky Sports.
"Apart from the match against Granada, the team has been showing good things throughout January. (Against Sevilla) we played well and have given a bit of a rest to key players and the match comes at a good time for us."
On the extra day's rest, Karanka said: "We've proven it ourselves - it does show.
"But they (United) have a bit of a cushion (at the top of the Premier League) and I'm sure they'll be making rotations and resting important players."