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Former Portugal captain Costinha has been impressed with the "fantastic" performances of his compatriot Bruno Fernandes since his arrival at Old Trafford, and feels the midfielder can lead the Red Devils back to the very top of the game.
Fernandes joined United from Sporting C.P. during the January transfer window in a deal worth an initial EUR55 million (?47m/$60m) and has made an instant impact on Ole Gunnar Solskjaer's side.
The 25-year-old has contributed three goals and four assists in his first nine appearances for the club as United push for a place in the Premier League's top four as well as gunning for trophies in the FA Cup and Europa League.
And Costinha, who famously scored Porto's goal at Old Trafford to knock United out of the Champions League in 2004, believes that after struggling in his first appearance for the club, Fernandes has already proven his worth to a team in transition.
"He is a fantastic footballer," Costinha told Goal. "I don't know him as a person, but sometimes I message him on Instagram
"I remember his debut at United (against Wolves) and his socks were down after 70 minutes. I said to him: 'Don't worry about that.' I saw in his head he was tired and wanted to come off. He wasn't used to the rhythm. I just said: 'Don't worry, once you get used to that rhythm with all the intelligence in your head and ability in your feet then it will be easier for you'.
"He is making very good progress and he is playing very well for United. They need time after moving on from Sir Alex Ferguson under new leadership and with a different mentality, but they still play to win every tournament.
"The history of Manchester United tells you to win every tournament. If you go there, you have to win all the cups, and that includes the Champions League. You are talking about Man United - it is one of the biggest clubs in the world.
"How many players want to play for Man United? Many would love to play there. It is a fantastic club."
Costinha almost got the opportunity to do just that after he was approached by former United assistant coach Carlos Queiroz regarding a short-term transfer in late 2005.
United were in the market for a combative midfielder but were unable to strike a deal with Costinha's club at the time, Dynamo Moscow, given he had only moved to Russia six months previously.
It marked the second occasion on which a potential transfer to the Premier League had fallen through after his former boss at Porto, Jose Mourinho, attempted to bring him to Chelsea after he was appointed Blues manager in 2004
"Yes, I had two opportunities to play in England," he revealed. "The first one was when I could have gone with Mourinho to Chelsea, but then [Claude] Makelele stayed at the club. I don't think Mourinho wanted two players who were ambitious to play in the same position.
"If Claude was playing, I wouldn't have been happy, and if I was playing, then Claude wouldn't have been happy. Jose would have been happy because he could have two players he trusts!
"Porto didn't allow me to leave anyway. That summer, Jose Antonio Camacho also made an offer from Real Madrid for Ricardo Carvalho and myself, but I didn't go there either.
"After I went to Russia, I was in the airport in Frankfurt back to Moscow and I received a call from Carlos Queiroz of Man United," he continued. "At the time I think they had a lot of injuries in midfield and they wanted to sign me. He asked me if I wanted to go and I said yes.
"Of course, I was sad [it didn't happen] because it was Man United, but I had a five-year agreement [with Dynamo] and I couldn't fight them. I understood why the president didn't want me to go.
The first offer [from United] was a half-year contract from January to June. Then my agent got it up to a two-and-a-half-year contract. Dynamo Moscow had bought me and I had five years left on that deal, so they didn't accept the offer."