Mourinho left Porto a hero in 2004 after guiding the club to a shocking Champions League triumph before embarking on a career abroad.
After being sacked from his second visit to Chelsea more than a decade later, he nearly stepped in to help Porto with a short-term contract.
The Portuguese coach had already agreed to take the helm of United next summer, which ruined his hopes for a return, as da Costa said.
“We were without a coach in the middle of the season,” said da Costa to FC Porto em casa. “I approached Mourinho, who had a contract with Manchester United but was only going to start the following season, and asked if he could come until the end of the season before he moved to Manchester.
“It seemed impossible. But not for him, he said yes.
“There was a cup final at the time, a league cup final and he said he was coming.
“And when we thought it was possible, Manchester United did not allow it because they argued that we could be opponents in European competition.
“But many people ignore the fact that, without any conditions, Mourinho was available to spend half a season in Porto in the event of an emergency. “
“It is an unknown fact, but it shows the affection with which he was. “
Porto and United both started the 2015/16 Champions League campaign before being eliminated in the group stage to the Europa League.
The two teams withdrew from the competition in the first knockout rounds, but could have met at the quarter-final stage.
Julen Lopetegui was head of Porto until his dismissal in January, Mourinho being officially named boss of United the following May.
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Mourinho did not rule out a return to Porto in the future, but in an admission made after his dismissal from Man Utd last year.
“If I think the club is right, has the right structure and the right ambitions, I would have no problem coming back,” Mourinho said in an interview with Spanish newspaper AS.
“I think it’s a nice feeling when a club where you’ve worked before wants you to come back but the only club that has done it is Chelsea, so far no one else has done it. “