The Red Devils remain in the hunt for two trophies this season.
A date with Barcelona in the quarter-finals of the Champions League has been set, while they face Wolves in the last eight of the FA Cup on Saturday.
Success in either of those competitions would get United back on track, while they are also chasing down a top-four finish in the Premier League.
Matic is eager to see Ole Gunnar Solskjaer’s deliver on multiple fronts, while also halting the charge of arch-rivals seeking to secure domestic and European dominance.
“Man City are a great team and they are fighting for the title and, like us, in the Champions League and the FA Cup. For sure they will try to win everything but we are ready to compete with them.
“When you finish the season with a trophy it's different. We will try to do that.
“We have the Champions League to play and the FA Cup and Man United always wants to do the best that is possible. We want to be in the top four and we will try to do everything. We have the quality to do that.”
United are set to enter the international break sat outside the Champions League spots.
A 2-0 defeat at Arsenal saw them slip out of the top four, but Matic insists a rare off day for Solskjaer’s side in north London was a minor blip in an otherwise impressive run of form.
He added: “We didn't play badly against Arsenal. We created a lot of chances, we played some good football.
“But this is the Premier League. Every team has quality and we cannot win all the time.
“Of course we are not happy with the game that we lost but we know that we did some great things - and Saturday against Wolves is a great opportunity to bounce back.”