The Premier League club wants a new first-choice keeper and would like to sign Onana this summer.
He has kept eight clean sheets in 24 Serie A appearances this season. Stalwart Samir Handanovic was starting league games, but the 27-year-old took over between the sticks.
Onana also kept eight clean sheets in UEFA Champions League games to help his side reach the final.
He helped them win the Italian Super Cup and the Coppa Italia title in his debut campaign in Italy.
Onana signed for the Nerazzurri after leaving Ajax on a free transfer last summer. He has established himself in Milan.
However, he could be on the move again this summer, with Chelsea eyeing him to replace one of their goalkeepers.
Edouard Mendy was excellent for the club when he first signed but began to lose form early last year.
Mendy has struggled to get back to his best and will likely leave the club this summer.
Kepa Arrizabalaga has been a better performer this season but is still not up to the required standard. The Blues would rather sell him, but clubs don’t want to take on his massive wages.
If one or both of them will leave Stamford Bridge this summer, the Blues will step up their interest in Onana.
Inter will demand around €50 million for the former Barcelona youth goalkeeper.
After the Champions League final against Manchester City in Istanbul, Inter directors will meet with their keepers.
Handanovic’s contract expires this summer, and he is preparing to leave. He did not enjoy being number two this season but accepted the situation.
Inter don’t want their two keepers to leave in the same summer as they will need two signings to replace them.
- La Liga Weekly: Real Madrid thump Girona, Celta Vigo’s woes continue
- Ten Hag to drop Pellistri for midfielder | Expected Man Utd line-up (4-2-3-1) vs Galatasaray
- Double injury boost confirmed, Trossard starts | Expected Arsenal line-up (4-3-3) vs Lens
- Chelsea legend Frank Lampard opens up on the club’s struggles this season
- Feyenoord star Santiago Gimenez poised for huge summer move – where could he go?