The Blues have been tipped with a late interest in the Chile international, who looks set to leave Arsenal this month after being the subject of a reported £35m bid from the Red Devils.
Conte, though, does not believe the Chelsea board will look to land the 29-year-old while remaining tight-lipped over the west London giants' transfer plans for January.
Image: Manchester United's Henrikh Mkhitaryan to make decision on Alexis Sanchez move
Asked if Chelsea were actively seeking to sign Sanchez, Conte, speaking ahead of Wednesday's FA Cup third-round replay against Norwich City, said: "I don't know. I don't think so. I don't know, but I don't think so."
He added: "About the transfer market, I prefer to talk to the club, also to give opinions.
"I repeat: I don't want to give my opinion about the transfer market."