Oliver Giroud came on to score a brace in Chelsea's 3-2 comeback win against Southampton.
In January Giroud ended his five-and-a-half year stay with the Gunners when he joined Chelsea.
Sarri, who has done a brilliant job in Naples, has been mooted as a potential replacement, but Conte is not interested in discussing the situation.
Conte, who won the Premier League in his first season, dismissed the assertion his players have to produce a strong finish to help improve his chances of staying in charge.
Chelsea manager Antonio Conte has told his players to show their professionalism over the last few weeks of the season amid speculation he will soon be departing.
"As long as mathematically it is going to be possible, we are going to believe", said Giroud.
"We've got to stick our chests out, get on with it, start being men and take responsibility". Often, he has been the one highlight in a campaign beset by apathy.
It looked like another ritual defeat for struggling Chelsea, another bad day at the office for an impotent outfit.
"Our first half was very negative", said Chelsea boss Antonio Conte.
"But I saw a great reaction". They have to play for the club and the fans, to show great character like today.
"It's a clear red card and clear intent to hurt Shane", raged Hughes.
Using his famed prowess in the air, the France international headed the Blues back into contention after Chelsea had gone 2-0 down at St Mary's and then, after Eden Hazard had made it 2-2, it was the boot of Giroud that secured a win that had looked unlikely for long periods of the game.
Conte swiftly responded by hauling off the disappointing Alvaro Morata and Davide Zappacosta for Pedro Rodriguez and Giroud.
Whomever Chelsea land, however, it seems Conte's departure from Stamford Bridge appears increasingly likely, with the Italian admitting he is not currently planning for next season at the club.