The Argentine was sacked by Tottenham Hotspur in November after a poor start to the season, but he remains one of the most highly-rated bosses in European football.
According to the Sun, Real Madrid were eager to agree a deal with Pochettino to become Zinedine Zidane’s successor.
But the 47-year-old turned down the Spanish giants because he wants another Premier League job, this time in Manchester.
The United and City jobs are said to be the only two positions that interest the manager.
Pochettino is considered a leading contender to take over at Old Trafford by the Red Devils hierarchy, if Ole Gunnar Solskjaer is relieved of his duties.
And Pep Guardiola’s future at the Etihad remains uncertain amid speculation that he could leave at the end of the season.
The prospect of the two jobs becoming available has led Pochettino to turn down a lucrative offer of around £12 million from Real.
Both Manchester clubs have struggled to compete with runaway leaders Liverpool in the Premier League this season.
Defending champions City are third in the table and 14 points behind the title pace, with almost half of the season played.
United are further back in sixth place, four points outside the Champions League places and a massive 24 points behind their rivals from Anfield.
City host second-placed Leicester on Saturday as they look to cut the four-point gap to Brendan Rodgers’ surprise package.
United travel to rock-bottom Watford on Sunday in the final round of league fixtures before Christmas.
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