Coverage of the Spanish champions was dominated this week by a report in Marca sports daily that said club captains Iker Casillas and Sergio Ramos had threatened to leave along with several team mates unless Mourinho was dismissed.
Real president Florentino Perez said the newspaper was lying and trying to destabilise the club but Marca have stuck by their story, the latest in a string of reports suggesting all is not well between Mourinho and some of his leading players.
The combative Portuguese has drawn criticism this season with his side 15 points behind La Liga leaders Barcelona and they host their arch rivals on Wednesday in the first leg of their King's Cup semi-final.
Elimination followed by defeat to Manchester United in their Champions League last 16 tie would almost certainly end Real's hopes of silverware this season and increase the pressure on Perez to replace Mourinho, lured at great expense from Inter Milan in 2010.
Varane, Real's 19-year-old French centre back, was sent out instead of Mourinho on Saturday to give the news conference previewing Sunday's La Liga game at home to Getafe and said the coach had the players' full support.
"We are all behind the coach, who is the best in the world," Varane told reporters.
"The media are being tough on him but he is doing a good job and all this is not necessary."
Varane added that the squad had given Mourinho, who has barely spoken to reporters since the turn of the year, a signed photograph taken during the wild celebrations after they sealed the La Liga title by beating Athletic Bilbao last season.
Real have a number of injury problems ahead of the Getafe match and Wednesday's Cup game, with Casillas sidelined for up to three months with a broken hand and Varane's fellow centre back Pepe still recovering from ankle surgery.
"Losing Iker could destabilise the team but I don't think it will change all that much," Varane said.
- Sports & Recreation
- Iker Casillas
- La Liga