Fabregas, whose contract expires at the end of the season, appeared to bid farewell to English football on Saturday , taking time to wave to the Stamford Bridge faithful following the Blues' FA Cup win over Nottingham Forest.
Monaco boss Thierry Henry - a former Arsenal team-mate of Fabregas - confirmed on Monday the Ligue 1 side are talking to the 31-year-old and Sarri thinks the midfielder should go elsewhere and seek a contract longer than the one year on offer from Chelsea.
"At this club there's a rule, the renewal of players over 30 is for one year. I don’t want a player as important as Cesc unhappy."
Sarri claimed to be in the dark over suggestions Fabregas was already in Monte Carlo, adding: "I don't know, yesterday he had a free day for the injury, so I don't know."
When asked if Cagliari's Nicolo Barella could replace Fabregas at Stamford Bridge, Sarri replied: "I don't want to speak about players of other teams, of course
"If Cesc goes, we will, of course, need a replacement. With midfielders we are in trouble I think because of the situation of [the injured Ruben] Loftus-Cheek.
"If the situation is serious or not, without Cesc we have only five [midfielders]."
"Cesc can travel and have meetings with anyone," Henry told reporters.
"As you know, he had a standing ovation [in Chelsea's win over Forest] and there were some tears, because he gave so much to the Premier League.
"He's free. If we do it in July, we'll do it in July. It's true, though, that we are currently talking to him. We are waiting.
"We are talking about Cesc Fabregas, it seems that he'll leave Chelsea. But I guess that many teams would like to sign him.
"Since I left Arsenal, we talk every three days. That hasn't changed in the last few days."