The ex-Cameroon international has proven an adequate successor to Samir Handanovic in the San Siro goal and helped Simone Inzaghi's side reach the Champions League final in his debut season.
Onana kept five clean sheets in six knockout games leading up to the showpiece event, as well as a further three in the group stage to put him one behind Edouard Mendy, who holds the tournament's single-season record with nine shut-outs in 2020-21.
However, the 27-year-old missed out on a record-equalling night as Inter fell to a 1-0 loss to Man City, who clinched their maiden European Cup thanks to Rodri's second-half winner.
Nevertheless, Onana's performances in between the sticks have attracted plenty of attention, and Chelsea are thought to be pushing the hardest to bring the ex-Ajax man to the Premier League.
A recent report claimed that Onana had reached an agreement in principle over personal terms with Chelsea, who are supposedly willing to throw in two players as part of a deal.
However, speaking to the media after Inter's defeat in Istanbul, Onana insisted that he was "so, so happy" in Milan, although he could not guarantee that he would remain at the club if they opt to sell him.
"I'm so, so happy at Inter. At this professional level you never know what happens. I'm available for Inter, they decide and I will accept what they want. I'm happy at Inter," the shot-stopper said.
Onana ends his maiden campaign at Inter with 19 clean sheets from 41 appearances in all competitions, including eight shut-outs from 24 Serie A matches.
The former Ajax and Barcelona youngster has also impressed with his footwork throughout the season, and his qualities on the ball were lauded by City boss Pep Guardiola after Saturday's final.
"When you have a goalkeeper like Onana who can read perfectly where everyone is to pass to, with [Hakan] Calhanoglu and [Nicolo] Barella, then the strikers hold it up and move the ball around. It is very, very difficult. It would be a tiny bit easier without this goalkeeper, but still very tough," Guardiola said in his post-game press conference.
Chelsea could face competition from Manchester United for the signature of Onana, though, while Tottenham Hotspur have also been credited with an interest but are believed to be prioritising a move for Brentford's David Raya.
The Blues could not settle on an undisputed number one during the 2022-23 season, although Kepa Arrizabalaga was given the nod more often than not thanks to Mendy's lengthy absence with a finger injury.
Kepa lost his place in the team upon Mendy's arrival in 2020, but he kept nine clean sheets in 29 Premier League games this term as Chelsea finished 11th in the table.
Mendy is thought to be on the way out after rejecting an offer to extend his deal, but Kepa's long-term future is also unclear, as he seemingly failed to convince Chelsea that he should be their first-choice goalkeeper moving forward.