Manchester United have been regularly linked with a move for Rodriguez, who has endured a difficult campaign at Real Madrid.
The Colombia international has been limited to just 32 appearances under Zinedine Zidane – despite scoring 11 goals across all competitions.
Some reports have gone as far to say the 25-year-old could move to Old Trafford as part of a deal that sees David De Gea go the other way.
But journalist Carlos Antonio Velez, speaking to Radio Antena 2, says the player is not one of Mourinho's summer targets.
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Manchester United do not want to sign Real Madrid star James Rodriguez
Jose Mourinho does not want to bring Real Madrid star James Rodriguez to Manchester United
Express Sport understands he wants both Antoine Griezmann and Romelu Lukaku, while Nemanja Matic and Michael Keane have also been heavily linked.
However, Velez says that Rodriguez is not wanted because he thinks he does not fit the bill of a Mourinho player.
Though he rates the Colombia star highly, the journalist says that defensive work-rate is not one of Rodriguez's main attributes.
As he cannot operate well at both ends of the field, Mourinho is unlikely to pursue a move for him.
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The United manager is known to want his players to work hard in both defence and attack, something he has criticised current winger Anthony Martial for.
Jose Mourinho has criticised Anthony Martial for his work-rate
Real boss Zidane, meanwhile, explained yesterday that competition for places was why the player had not featured more often this season.
“A player like him would have liked to have played more this season, but I have to decide," he said.
“He’s been very important throughout the season and when he’s played, he’s done very well.”
Rodriguez could feature when Real go up against Juventus in the Champions League final on Saturday.