Carlo Ancelotti is currently in the Real Madrid hot seat, and he has a contract with the club until June 2024
However, there is a belief that he could leave the reigning European champions at the end of the season amid links with the vacant Brazil managerial position.
Ancelotti recently revealed that he was "very excited" to be wanted by Brazil's interest in appointing him as their head coach.
With Ancelotti's Real Madrid future shrouded in uncertainty, a number of names have been touted as his potential successor.
Julian Nagelsmann and Mauricio Pochettino are both believed to be on Real Madrid's radar, although the pair are also being linked with Chelsea and Tottenham Hotspur.
According to journalist Antonio Romero, Real Madrid have not ruled out the prospect of Mourinho returning to the club.
Speaking to Cadena SER about the prospect of Real Madrid Under-19 coach Alvaro Arbeloa becoming assistant manager to a new head coach, Romero also revealed that Zinedine Zidane could return.
"I think that in Madrid they are very interested in promoting Arbeloa," Romero said. "There are other positions in the club that are very interesting, such as the second coach of the top dog to arrive next season.
"They tell me not to rule out Mourinho, and although it seems like science fiction, today it cannot be ruled out. Another name they tell me is Zidane."
Mourinho previously coached Real Madrid between 2010 and 2013, winning a La Liga title, a Copa del Rey and a Spanish Super Cup.
The 60-year-old ended Roma's 14-year trophy drought last season, guiding the Italian side to the inaugural Europa Conference League trophy.
Roma, who are currently sitting in fifth place in the Serie A table, are chasing Champions League football and are in the quarter-finals of the Europa League.
Mourinho has a contract with the Giallorossi until June 2024, and it is unclear whether he would consider returning to Real Madrid.