The goalkeeper has starred during the Nerazzurri’s unlikely run to the Champions League final, keeping eight clean sheets in 12 games in Europe’s elite club competition.
Chelsea are interested in a move for the former Ajax stopper and Standard Sport understands the Blues are eager to discuss a deal with the Italian giants.
Either Kepa Arrizabalaga or Edouard Mendy could be offered in part-exchange although it remains to be seen if Inter would be interested in a swap deal or hold out for a larger transfer fee.
Incoming Blues boss Mauricio Pochettino is thought to be keen to sign a new goalkeeper and a number of options have been explored.
Brentford’s David Raya, Borussia Dortmund’s Gregor Kobel and Valencia’s Giorgi Mamardashvili are among some of the other targets considered.
Speaking to TV Play in Italy, Onana’s agent Albert Botines said: “Transfer market rumours are normal at this stage, but I prefer not to talk about it because it’s very early and now the boy is focused only on the pitch,” he said.
“We have a five-year contract with Inter. He has another four years on his contract and now he is focused only on the Serie A final and the Champions League final.
“He still has a long contract, don’t worry. He’s very happy, he’s playing for the strongest team in Italy.”