The 27-year-old caught the eye of several European giants during his time at Ajax, although a lengthy doping ban initially harmed his prospects of a move elsewhere.
Onana ultimately ran down his contract with the Amsterdam giants and joined Inter on a free transfer last season, and he had big gloves to fill in the shape of Samir Handanovic.
However, the former Cameroon international - who called it quits with the national team after a World Cup row with manager Rigobert Song - has enjoyed a stellar first season at San Siro, keeping 19 clean sheets in 40 appearances.
Onana's exploits helped Inter reach the Champions League final, where they will do battle with Manchester City in Istanbul on Saturday night, and the shot-stopper will endeavour to match a pair of competition records at the Ataturk Olympic Stadium.
Onana has impressively kept five clean sheets in six knockout games for the Nerazzurri, who could match Arsenal's single-season record of six knockout shut-outs from the 2005-06 season.
The Cameroonian also needs just one more clean sheet to match Edouard Mendy's record of nine in total from the 2020-21 season, and the Chelsea man could potentially now make way for his African counterpart.
Despite his affirmation that he is happy in Milan, Tuttomercatoweb claims that Onana is keen to test himself in the Premier League, and the Inter number one has now given the green light to a move to Stamford Bridge.
However, the report adds that Chelsea's opening offer of €40m (£34.2m) was rejected by Inter, who have Onana under contract until 2027 and are therefore under no pressure to sell for a cut-price fee.
Manchester United and Tottenham Hotspur could also rival Chelsea for the signature of Onana, whose possible arrival in West London would likely push at least one of Mendy or Kepa out of the door.
Having been demoted to second choice upon Mendy's arrival in 2020, Kepa - who remains the world's most expensive goalkeeper - won over Graham Potter and Frank Lampard in the 2022-23 season, although he was helped by the Senegalese's lengthy absence with a finger injury.
However, Kepa and Mendy's efforts combined could only help Chelsea finish 11th in the Premier League table, and manager Mauricio Pochettino is supposedly ready to do away with one of them in the summer window.
Mendy is thought to be the more likely to head for the exit door at this moment in time, having rejected the chance to extend his contract at Stamford Bridge beyond the summer of 2025.
Brentford's David Raya, Valencia's Giorgi Mamardashvili and AC Milan's Mike Maignan have also been named as possible goalkeeper targets for Chelsea, who also have Marcus Bettinelli and USA youngster Gabriel Slonina in the ranks.