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The Red Devils on Tuesday announced that a deal in principle had been agreed to sign Varane from Real Madrid.
According to reports, United have agreed an initial fee of £34m to bring the 28-year-old French centre-back to Old Trafford.
Solskjaer has already bolstered his squad options ahead of the new Premier League season with the free transfer of Tom Heaton and sensational £73m acquisition of Jadon Sancho.
Varane, who is expected to sign a four-year deal with United, has been widely tipped to replace Lindelof in the heart of the Red Devils' defence.
However, Solskjaer is not ready to drop Lindelof out of his plans and will instead integrate him into the backline with Varane and United captain Harry Maguire.
The Athletic reports that United are happy with the 27-year-old Swedish centre-back's performances.
And Lindelof could be deployed in a trio alongside Varane and Maguire, despite Solskjaer usually opting for a back four featuring Luke Shaw and Aaron Wan-Bissaka.
Solskjaer is keen to keep the United star in the first-team selection and values Lindelof's forward-passing ability.
The United manager is expected to reinforce his defensive options further as the Red Devils continue their summer spending spree.
Atletico Madrid star Kieran Trippier is reportedly a top target for United, with Solskjaer wanting to add competition for Wan-Bissaka at right-back.
Rennes midfielder Eduardo Camavinga has also been heavily linked with a move to Old Trafford amid uncertainty surrounding Paul Pogba's United future.
Varane, whose current Madrid deal expired in 2022, won three La Liga titles, four Champions Leagues and a Copa del Rey during his decade at Los Blancos.
Madrid confirmed in an official announcement that they had agreed a transfer with United for the 2018 World Cup winner, saying they "wish him the best of luck in this new stage of his career."
Featured Image Credit: PA
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