Terry is seeking a new club after his switch to Spartak Moscow went up in smoke.
But the Chelsea legend is still on the radar of Championship sides and could move to England’s second tier.
Sarri spoke about a potential deal with Terry on Friday after it emerged the defender has rejected a move to Russia.
“It is up to him,” the Italian told reporters. “If he wants to play for another season, it is right he tries to play.
“If he wants to help us I am really very happy.
“He told me he wants to play but I don’t know, I have to speak to him.
“Chelsea is his home. Of course I am open [to having] him because of his history with the club. He has won everything with the club so it is up to him.
“Here he is a point of reference, here it is John Terry’s home so he will be very important for everybody, only the presence.”
Despite Sarri’s words giving confidence to the idea of Terry returning to Stamford Bridge, a deal with Aston Villa is supposedly still on the cards.
Chelsea are now 8/1 to re-sign their former captain.
That is according to bookmakers Coral.
“The odds on a return to Stamford Bridge for John Terry have collapsed in the last 24 hours and although it still looks more likely that the former England defender will sign for a Championship club, many punters are backing him to re-join Chelsea,” said Coral’s John Hill.
Terry can sign a deal with an English club outside of the transfer window as he is a free agent.
A proposed move to Derby was snubbed out by Rams manager Frank Lampard said he cannot fit his former team-mate in his squad.
“John is a fantastic leader, a fantastic player and he’s got a lot to offer,” Lampard said. “But we have options in defence, so there’s no more movement from us.
“John will be great wherever he goes, wherever he chooses or whoever chooses him.”