Mourinho’s attempts to sign Leicester City’s Harry Maguire, Toby Alderweireld from Tottenham all failed.
The Red Devils boss criticised Manchester United’s board’s transfer dealings publicly and has had a difficult start to the season.
With Maguire signing a new long-term deal with Leicester City, and Alderweireld reestablishing himself in the Tottenham team, Mourinho may have shifted his attention to the Chelsea former captain.
The newspaper reports that the Portuguese will monitor the situation of former England defender Cahill over the next few months, with a view to possibly signing him from Chelsea in January.
Mourinho worked with Cahill at Stamford Bridge and knows the player too well.
Cahill has made just one Premier League appearance this season and has also attracted attention from Championship clubs Sheffield Wednesday and Aston Villa, according to the newspaper.
The former England star is currently behind David Luiz, Antonio Rudier and Andreas Christensen in the pecking order at Stamford Bridge.