The England international was the subject of a failed bid by Chelsea on Tuesday, with United re-iterating their stance that the forward is not for sale.
Rooney is reportedly unhappy at comments made by new United manager David Moyes regarding his role at the club, after he suggested Netherlands international Robin van Persie will be the club's first-choice striker this season.
But Docherty, who managed Chelsea as well as United during his career, believes Mourinho going public with his admiration for the 27-year-old has heightened the player's mentality.
"It's a case of ducking and diving, I think it's Mourinho stirring it up a little bit," Docherty told OMNISPORT.
"We all know Rooney's a world-class player, no one has to tell us that.
"But Mourinho says: 'he's a world class player but I'm not allowed to to talk about players at other clubs', but he is talking about player at other clubs.
"(But) that's always been the case over the last 20 years, nothing changes. We all tap players up when your own players go away on international duty, you ask them to have a word with 'Joe Bloggs' to see if he'd like to come to Manchester United.
"That's been going on for the last 20 years, so that will not change."
The 85-year-old also feels the situation is difficult for Moyes, after missing out on Thiago Alcantara to Bayern Munich, with Cesc Fabregas also set to rebuff interest from Old Trafford.
"It adds pressure on Moyes because the supporters will be looking for a new signing, not to replace Wayne but to go along with Wayne," he continued.
"They're talking about the boy (Leighton) Baines at full-back in place of (Patrice) Evra, but Evra has been outstanding for Manchester United.
"So if the boy Baines comes what are they going to do with Evra?"