The Bayern Munich midfielder could be available to buy at the end of the season, despite having one year remaining on his current contract.
According to Chilean journalist Maks Cardenas, there is a chance Vidal could follow international team-mate Alexis Sanchez to Old Trafford.
United completed the deal for Sanchez yesterday in a move which saw Henrik Mkhitaryan switch to Arsenal.
The Red Devils are expected to lose Marouane Fellaini at the end of the season, while Michael Carrick will retire, so Vidal is seen as the perfect replacement.
Meanwhile, Chelsea are hoping to bolster their midfield following Tiemoue Bakayoko’s disappointing start to his Blues career.
Cardenas wrote on Twitter: “Arturo Vidal will remain at Bayern Munich for the rest of the season.
“In June you will still have one year of contract.
“He has offers from Italy and China.
“Chelsea and Manchester United also interested.”
Vidal yesterday congratulated Sanchez for securing a transfer to Man Utd.
He told FOX Sports Chile: “The teammates that I have are of great quality, important players who are doing things well on their teams and that has always a prize to reach the best teams in the world.
“Alexis has earned his chance to be at United, and I hope he goes on to win many titles with them.”