The 21-year-old France star has caught Jose Mourinho's eye as the Blues boss looks to strengthen his backline, the Daily Star reports.
Chelsea have yet to replace David Luiz, who joined Paris Saint-Germain for £50m, and Varane is said to be on the Stamford Bridge radar.
However, Manchester United legend Ferdinand, who signed for QPR in the summer, has put his own valuation on the player.
Mangala 31m & Luiz 50m...how much would Varane cost with these valuations at the moment ??! 60-70m??— Rio Ferdinand (@rioferdy5) August 12, 2014