The France international is believed to have already agreed personal terms with the Red Devils, as he is keen on a move to the Premier League at this stage of his career.
However, according to The Mirror, Man United are struggling to settle on a transfer fee with Real Madrid, who want £50m for the World Cup winner.
The report claims that Ole Gunnar Solskjaer's side are, as it stands, only prepared to pay £40m, and it is unclear whether either club will be willing to budge.
Varane's current deal at the Bernabeu is due to expire next June, and Los Blancos are thought to be resigned to losing him during this summer's transfer window.
The 28-year-old arrived at his club's pre-season camp on Friday morning to undergo a series of medical examinations but was not involved in any training sessions, as he continues to recover from his participation in this summer's European Championship with France.