The Red Devils are reportedly willing to offer the Wales international a salary worth £16.7million a year - after tax.
United have long been linked with a move for Bale - David Moyes was reportedly prepared to pay a world-record fee for him in 2013 and Louis van Gaal is said to have made an enquiry last year.
That is according to The Mail, who claim the Italian has earmarked the pair - both 23 - as potential successors to John Terry, 35.
The Blues are said to be on the look out for English talent in the heart of defence to keep up with the Premier League's homegrown player regulations.
GETTY
Chelsea wnat Ben Gibson and Michael Keane
GETTY
Kieran Gibbs to leave Arsenal this January
Bookmakers BetStars have priced Arsenal defender Kieran Gibbs at 10/11 to leave his boyhood club when the transfer window reopens in January if his playing situation doesn't improve.
“After heavy backing in the last 24 hours, Kieran Gibbs is now odds-on at 10/11 to end his 12-year stay at Arsenal this January as he looks for first-team opportunities elsewhere,” said a BetStars spokesman.
“After falling behind Nacho Monreal in the pecking order, we expect Gibbs to follow fellow Englishman Jack Wilshere by joining another Premier League club in hope of regaining his place in the England squad.”
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