Jones moved to Old Trafford from Blackburn Rovers in June 2011. Several of Europe's top clubs, including United and Paris Saint-Germain, had expressed an interest in signing Varane from Lens at that time before he opted to join Madrid.
The France international says that he rejected a move to United because of Jones's recent arrival.
Varane told L'Equipe: "Manchester United? They had just signed Phil Jones in my position.
"PSG? The project there wasn't clear. The Qataris had only just arrived and it was all very vague.
"My first reaction when Real wanted to sign me was not, 'Of course I will go'. I only made my decision when I knew that the coach wanted me to play in the first team."