The left back, 21, has found himself down the pecking order behind Ashley Young, Luke Shaw and Marcos Rojo at Old Trafford.
And despite featuring during pre-season, he has not been in a matchday squad for either of United's fixtures against Leicester or Brighton.
Mitchell is set to move back to Tynecastle, where he spent the second-half of last season on loan at the Scottish Premier League club, but reports also claim he has signed a new deal at United till 2020.
The left-back and left winger missed much of March and April with a knee injury, which was thought at the time to be season-ending.
But he fought back to fitness and played two of the final three games of Hearts' season.
Hearts boss Craig Levein told the Scottish Sun: "We're nearly over the line with Demi.
"We need another centre-back although I thought the two young boys at the back were excellent."
Mitchell impressed Jose Mourinho and the Manchester United squad with his rendition of a Drake song during pre-season training in Los Angeles.
He featured in United's International Champions' Cup matches against Liverpool, Real Madrid and Bayern Munich, but did not get a look-in once the Prem season started and has yet to add to his single competitive first-team appearance.
The resurgence of Shaw, 23, so far this season has also impressed Mourinho and the Englishman was one of few bright sparks in their defeat to Brighton.
Full-back Diogo Dalot is also set to be fit soon, further crowding those positions for the Red Devils.
Derby boss Frank Lampard was also interested in bringing in the England Under-20 international on a permanent £500,000 deal, but United were unwilling to sell.
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