While Arsenal were in West London for the first leg of their EFL Cup semi-final, Conte and Sanchez had a conversation in the tunnel at Stamford Bridge.
However, despite acknowledging his admiration for the Chilean international, Conte has claimed that he will not enter the race to sign the attacker, who has just six months remaining on his Gunners contract.
The 48-year-old told reporters: "I said hello. He is a great player, he knows very well that in Juventus I tried to buy him from Udinese but he went to Barcelona. He knows very well my admiration for him. So it was a good chance to say hello to him.
"No other situation or conversation. I repeat for sure I have great admiration for players and he is one of them. I stop."
Manchester United are said to have agreed financial terms with Sanchez, who is also interesting Manchester City.