But relations with Spurs have been rocky ever since United’s infamous capture of Dimitar Berbatov in 2008.
United managed to snap up the Bulgarian despite Manchester City agreeing a deal with Spurs first.
As a result, Tottenham have since blocked Gareth Bale and Luka Modric leaving for United.
And with a move for Rose now also looking unlikely, the Daily Record say Mourinho is eyeing a younger defender.
Celtic’s Kieran Tierney is one name on his list.
The Scotland international has taken the Premiership by storm with Liverpool and Arsenal also linked.
In August, Hoops legend John Hartson claimed Mourinho was a huge admirer.
“I’m hearing he’s Manchester United’s number one target,” he said.
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Man Utd news: Jose Mourinho has now changed his transfer plans
“But why on earth would Brendan Rodgers sell Tierney right now?
“If I’m Brendan Rodgers, I’m saying to Mourinho, ‘Let him have another season here, keep your £25-30m for now, he’s got Champions League football, he loves playing for Celtic’.
United are also keen on Fulham’s 17-year-old star Ryan Sessegnon.
Yet Tottenham are likely to provide competition for the teenager’s signature.