The Serbia international has made 163 appearances for the Serie A side since a switch from Belgian side Genk in 2015, helping the club win the Coppa Italia in May.
But Italian news outlet Corriere dello Sport report that the 24-year-old’s agent – former Chelsea striker Mateja Kezman – has been in London and has reached an agreement with the Red Devils.
However, it’s claimed a transfer will only happen if Paul Pogba leaves Old Trafford before the transfer window shuts on August 8th.
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The Frenchman’s future at the club remains uncertain having been linked with a move away and it’s thought United have put a £150million price-tag on their midfielder.
If the World Cup winner was to seal a big-money switch Ole Gunnar Solskjaer would put some of the funds towards bringing in Savic, who’s valued at £80million, as a replacement.
It’s reported that the Serbian would receive an annual salary of £5.4million per year over a five-year deal with United.