Thursday's 3-0 win over Malmo at Stamford Bridge put Chelsea into the last 16 of the Europa League 5-1 on aggregate and relieved some of the pressure on Sarri, but he still had to answer questions about the Roma links after the match.
"I have a contract with Chelsea for the next two seasons so it is impossible to have another contract," he told BT Sport.
"I read in an Italian newspaper something about a meeting with (Roma advisor) Franco Baldini but I think for the moment Franco is in South Africa, so it is very difficult."
Another figure at Chelsea feeling the heat is midfielder Jorginho, who was booed by the home support when he replaced goal scorer Ross Barkley in the second half.
Sarri came to the Italy international's defence.
"I think that in the first 30 minutes we understood why Jorginho is very important for our team," Sarri told reporters. "We were in trouble to exit from our half with the pressing.
"With Jorginho, it is easier, I think. I would hope that our fans would be able to understand that Jorginho for us is really a very important player."
Chelsea next play Manchester City in the League Cup final at Wembley on Sunday.
(Reporting by Rohith Nair in Bengaluru; Editing by Peter Rutherford)
