Mbappe is recovering from a knee injury and while he won't be fit for the clash with Elche this week, Arbeloa says the France ace will be with the squad for the second-leg of their Champions League round of 16 clash at City.
He said, "It's not a difficult time, he's getting better every day and his progress is going according to the plan we made when we decided to stop and we did the tests. He's doing very well.
"He won't be available tomorrow, but we're confident he'll be ready to travel to Manchester."
Real Madrid will go to City defending a 3-0 lead from the first-leg.
Meanwhile, on facing Elche, Arbeloa said: "We're approaching this match with the mindset that we're playing for the league title. It's a crucial game at home, and we want a similar atmosphere to Wednesday's.
"Our opponents play very well, better than their points tally suggests. They made it difficult for us in the first leg, and we're prepared to make an extra effort, knowing how tough the opponent is. Our only focus is winning against Elche."