The Champions League winners are believed to be keen on the Blues’ midfield maestro, and have been pondering a £25m offer for after the World Cup.
However Jose Mourinho will only allow the Brazilian to leave if he can bring in Modric.
The Croatia international was a key man under ‘The Special One’ while he coached Los Blancos, with his metronomic passing abilities having one the Portuguese’s heart.
Despite a deal for Cesc Fabregas having been tied up, Mourinho is keen to add Modric to his ranks as a replacement for Ramires.
Chelsea are likely to allow the move to go through, with the Londoners having been linked with the former Tottenham man on a number of occasions over the course of the past few years.
Varane is also on Mourinho’s radar following the sale of David Luiz.
The young Frenchman is currently one of the world’s most highly-rated young defenders and has been described as fantastic talent by the Chelsea chief.