France star Varane, 28, looks set to join Jadon Sancho at Old Trafford, after United reached an agreement with Borussia Dortmund to sign the England winger for £72million.
The Red Devils are getting their transfer business done early, having learned from last summer when they spent the entire transfer window chasing Sancho, but were priced out by Dortmund's £108m valuation.
Varane would add huge experience to the United backline, having won three La Liga titles and three Champions Leagues during his decade at the Bernabeu.
And his expected exit will also force Madrid into a defensive rebuild - with Carlo Ancelotti's side now expected to target Solskjaer's second-choice option.
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But sources have told ESPN that the Red Devils are confident of signing Varane for around £42m, rather than the £60m initially wanted by Madrid.
The French centre-back's exit would leave Los Blancos short of defenders, with skipper Sergio Ramos expected to join PSG after becoming a free agent.
And Torres is now top of Madrid's last to fill the void, with the defender preferring to stay in Spain rather than be tempted by Premier League interest.
One thing could scupper a move for the centre-back to the Bernabeu - and that's if Madrid decide to move for either Kylian Mbappe or Erling Haaland.
If Madrid were to decide that making a huge 'galactico' signing was their priority, Torres would have to wait until 2022 to join the La Liga giants.