Chelsea manager Antonio Conte is ready to let the Serbian leave Stamford Bridge but would prefer him to move abroad.
The Sun claim Matic has been training alone as the Blues continue their pre-season preparations.
Tensions between Chelsea and United have risen after Romelu Lukaku opted to move to Old Trafford instead of returning to Stamford Bridge.
Starsport reported last month that the Red Devils had a £40m agreement in place to sign Matic.
And Jose Mourinho is still keen on that deal happening with a midfielder now top of his shopping list.
Inter Milan are also interested in Matic and Conte would prefer the midfielder to make the switch to Serie A instead of a Premier League rival.
Chelsea have been trying to negotiate a new contract with the 28-year-old for 18 months but now look set to cash-in.
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Matic will be allowed to leave despite incoming man Tiemoue Bakayoko unlikely to be available until September through injury.
The Monaco midfielder is expected to complete his switch to Chelsea in the next few days.
The Blues have made two new additions this summer so far.
Goalkeeper Willy Caballero and defender Antonio Rudiger have joined Chelsea as they prepare for a return to the Champions League.
