Onana was a stalwart of Erik ten Hag at Ajax before both men left Amsterdam in 2022, as the former transferred to Inter while Ten Hag took the reins at Old Trafford.
A lengthy doping suspension had placed Onana's career on hold in 2021, but he proved a worthy successor to Samir Handanovic at San Siro as Inter reached the Champions League final.
The ex-Cameroon international kept eight clean sheets in the competition before the Nerazzurri lost 1-0 to Manchester City at the final hurdle, while he also helped Inzaghi's men win the Coppa Italia and Supercoppa Italiana.
Onana remains under contract with Inter for another four years, but Man United boss Ten Hag is said to be pushing for a reunion with his former number one in the wake of David de Gea's exit.
A recent report claimed that Man United are hopeful of wrapping up a deal to sign Onana this week, having already agreed personal terms with the Cameroonian shot-stopper, but they have so far failed to meet Inter's £51m valuation.
Where there is yet to be a significant breakthrough in negotiations, Man United are still said to be confident of getting a deal over the line, and Inzaghi has refused to guarantee that Onana - who is set to return to pre-season training today - will still be at the club next term.
"He's an Inter player, tomorrow [Thursday] he'll be among the players called up for pre-season. We know the transfer window is unpredictable and that all Italian clubs have to sell before they can buy," Inzaghi said.
"We know there's this risk [that he leaves] but at the same time, I'm calm about it all because the club and the owners have reassured me that this year we'll have a competitive Inter."
Inter are believed to be considering Tottenham Hotspur's Hugo Lloris and Bayern Munich's Yann Sommer as possible replacements for Onana, and Inzaghi entertained talk of a new goalkeeper arriving, stating that any new shot-stopper must be equally adept with the ball at their feet as they are with their hands.
"The goalkeeper will have to be technically good, so together with the club we're looking to find not just one but somebody else too," the Nerazzurri coach added.
"Over the last couple of years at Inter, first with Samir and then with Onana, we were able to count on goalkeepers who were very good with their feet. In my last year at Lazio too I had Pepe Reina, so the goalkeeper will definitely have to have that skillset."
Man United were locked in discussions with De Gea over a new contract, but an agreement could not be reached, and the Spaniard confirmed last weekend that he would be ending his 12-year stay at Old Trafford.
The Red Devils could also lose Dean Henderson to Nottingham Forest in a permanent deal, leaving Tom Heaton as their only senior goalkeeper, but Sean Dyche is said to be keen on reuniting with his former Burnley number one at Everton.
Heaton's contract at Man United only runs for another season, but Ten Hag is unlikely to let him depart if Henderson's expected exit goes through, and Luton Town are also said to have seen a bid to sign the 37-year-old blocked this summer.