Roberto Martinez was this week appointed as successor to Fernando Santos, whose tenure as Portugal boss came to an end after a shock FIFA World Cup quarter-final defeat to Morocco last month.
Spaniard Martinez took over not long after leaving his role as head coach of Belgium after its failure to advance from the group stage in Qatar.
Mourinho, who was tipped to return to his homeland and take charge of the national team before Martinez was appointed, revealed Portuguese Football Federation president Fernando Gomes made it clear he was the man he wanted to replace Santos.
The Roma boss has expressed his gratitude to Gomes, but says he did not want to turn his back on Serie A club Roma.
He said: "I would like first of all to thank the president of the federation. What Fernando Gomes told me made me very happy and made me proud.
"He said that I was not only the first choice as the new national coach, but also that I was his only option and that's why he would do anything to bring me back home.
"It was an honour, but in the end I decided not to accept. I'm here in Rome, that's what counts."
Mourinho, who has also been linked with the vacant Brazil job, signed a three-year deal when he was appointed as Roma head coach ahead of the 2021-2022 season.