Inter boss Antonio Conte is in the hunt for a new midfielder after losing a number of key players to injury in recent weeks.
Stefano Sensi, Nicolo Barella and Roberto Gagliardini are all facing time on the treatment table and Conte is keen to bring in reinforcements at the first opportunity.
That will be when the transfer window re-opens next month and reports are rife suggesting that Matic is being lined up as a new signing.
The Nerazzurri do not have a great deal of cash to spend on new players, and the fact that Matic should be available for a decent price, makes him an attractive option.
The Serbian is out of contract at the end of the season and with there being no sign of him penning a new one, he will be able to leave for a free in the summer.
However a fee could be agreed to get the deal done in January and Conte is keen to get the deal over the line.
The Inter boss knows him well from his time in England, and at the age of 31, he still has some of his best years ahead of him.
Matic has slipped out of favour at United, making just three Premier League appearances this season and he could jump at the chance of a fresh start at the San Siro.
Inter are joint top of Serie A with Juventus, but their title hopes could be hit during the remainder of the season if Conte is unable to bolster his ranks in the window.