The former Ajax shot-stopper left a trophy-laden seven years in Amsterdam behind in the summer to join the Nerazzurri, with a view to becoming Samir Handanovic's successor.
Slovenia veteran Handanovic remains on the books at San Siro, but Onana quickly became the club's new number one and has 14 clean sheets under his belt from 29 games this term.
The 26-year-old has played every minute of Inter's Champions League campaign to help the Nerazzurri set up a quarter-final tie with Benfica, as well as starting 18 games in Serie A.
Inter tied Onana down to a five-year contract until 2027 upon his arrival in the summer, but their long-running financial problems have alerted clubs to their highly sought-after talents.
According to Gazzetta dello Sport, Inter would not be in a position to turn down an offer of €40m (£35.2m) for Onana, and Chelsea have identified the ex-Cameroon international as their top goalkeeping target.
The Blues' chief scout was reportedly in attendance to watch Onana during Inter's Champions League quarter-final second leg with Porto, whose own shot-stopper Diogo Costa is also earning admirers from West London.
Simone Inzaghi's side are yet to receive any firm offers for Onana, but they are braced for bids to come through in the summer, and the goalkeeper can expect a significant rise on his yearly €3m (£2.6m) salary in the Premier League.
However, Chelsea could face competition from Manchester United to sign the former Barcelona starlet, with Erik ten Hag keen on a reunion with his old Ajax protege.
The Premier League duo have seemingly been handed an early boost in their pursuits of Onana, though, as Inter have identified Empoli's Guglielmo Vicario as a possible successor.
Chelsea boss Graham Potter had Kepa Arrizabalaga and Edouard Mendy battling for the gloves upon his arrival at Stamford Bridge, and the Spaniard quickly demoted his colleague to the bench.
Kepa has retained his place in between the sticks during Mendy's absence with a fractured finger, and the Blues are supposedly now willing to cut their losses on the Senegal international.
Mendy is believed to have rejected the chance to sign a new contract with Chelsea, who are now open to offers for the former Rennes man, and a reunion with Thomas Tuchel at Bayern Munich could be on the cards.
Meanwhile, Kepa - who remains the world's most expensive goalkeeper - is out of contract in 2025, and his long-term future remains clouded in uncertainty as the Blues aim to bring in a new number one.
Kepa made his 14th successive Premier League start in Saturday's clash with Aston Villa, but it was a miserable affair for the Blues, who lost 2-0 courtesy of Ollie Watkins and John McGinn's goals.
Potter's men have fallen below the Lions into 11th place in the table and now prepare to host Liverpool on Tuesday evening.