Manchester United boss Ole Gunnar Solskjaer looks set to take charge of the Red Devils permanently at the end of the season and he already has one eye on transfer targets.
United are confident they can prise the England star away from the Foxes in a deal worth £65m with Woodward ready to splash the cash.
But reports in Spain claim they are also pursuing an ambitious move for Varane – who would cost in excess of the £75m Liverpool paid to make Virgil van Dijk the world’s most expensive defender.
Varane is said to be considering his future at the Bernabeu and he will not be short of admirers come the end of the season.
Spanish publication OK Diariao claim PSG have already made it clear they will fork out €100m (£86m) for his services.
But news of PSG’s plans has got back to United and Bayern Munich with both clubs also willing to match their offer in a bid to snap up Varane.
News of United’s interest comes amid:
A player of Varane’s calibre rarely becomes available but the Red Devils will be looking to finally land him having been linked with him in the past if he makes it clear he wants to call time on his time with Real.
Jose Mourinho made no secret of his admiration for the talented 25-year-old but Los Blancos refused to consider selling him to the Old Trafford club.
It remains to be seen if the European Champions will consider selling Varane in the summer with the Frenchman still under contract until 2022.
Varane has refused to discuss his future in public though.
“I do not want to talk about my future,” Varane – who is preparing for Euro 2020 qualifiers against Moldova and Iceland – told Le Parisien .
“I am not one to discuss my future publicly.”
However, he did voice his delight at the news of Zinedine Zidane’s return to management this month as the French boss looks to get Real back on trac following a disastrous 10 months since he left.
“Nine months is not a long time. It was as if it was yesterday,” Varane added.
“I appreciate him both as a person and as a coach. He has been very important to me.”