Conte appeared to try and dampen speculation over Chelsea’s move for Sanchez.
But his words are not likely to kill off the reports that the Blues are keen on a deal.
Asked about Sanchez, Conte coyly said: “I don’t know, I don’t think so.
“About the transfer market I prefer to talk to the club and give an opinion and I repeat I don’t want to give my opinion on that.”
Conte had an infamous showdown with his Chelsea bosses last summer when they laboured to sign his top transfer targets.
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Chelsea entered the race to sign Sanchez on Monday after expressing their interest in the forward.
Arsenal are determined to get as much as they can for the Chilean, who has refused to sign a new contract.
Express Sport understands Manchester United remain frontrunners to sign Sanchez, with a £350,000-a-week contract in place for the 29-year-old.
Chelsea are seeking a new striker to add firepower to their forward line, having added just one player – Ross Barkley – to the side this January.
Asked if he is happy with his squad, the Italian added: “I try to work with my players, I am very happy to work with them and we are looking to build something important for this club.
“If someone asks me my opinion on if we need to improve then I give my opinion. The most important thing is to work and improve every single player.”
Michy Batshuayi appears set to leave the club on loan, with Sevilla said to be keen on the Belgian.
But Conte says the Belgium international will be involved in Wednesday’s FA Cup clash with Norwich.
“He is Chelsea’s player and he is in our squad,” Conte said.
“Tomorrow he has to play. I think this is the truth until now.
“He is a Chelsea player and is having the possibility to show that he can play for Chelsea.
“This is the reality, in the future I don’t know what will happen.”
There are also reports that Andy Carroll is being monitored ahead of a loan swoop – although West Ham would likely fight to keep their centre-forward.