The England Under-21 defender is to complete a loan move to Parkhead.
The 21-year-old has been told by United that he can leave on loan, and a deal has been struck with the Glasgow giants and he is now due to undergo a medical.
Blackett has played nearly a dozen first-team games for United, featuring a number of times last season for Louis van Gaal's side.
But he has slipped down the pecking order at Old Trafford this term and is being allowed to leave on loan for the season in an effort to get regular game time under his belt.
Blackett has two years left on his current deal with United, and his arrival could very well pave the way for Virgil van Dijk to leave Celtic - with Southampton leading the chase for the highly-rated Dutchman, as reported by the Daily Mail.
The Scottish Premiership champions are reluctant to part with any of their key men before the transfer deadline passes, but they have at least been able to bolster their ranks if a sale is to be sanctioned.