The Red Devils are now said to be "really close" to securing the signing of Onana, who has already agreed personal terms with Erik ten Hag's side as Inter brace themselves for another bid.
Onana arrived at San Siro last year with a view to succeeding Samir Handanovic long-term, as the Slovenia international will turn 39 in six days' time and became a free agent at the end of June.
Handanovic could yet pen a new deal with the Nerazzurri if Onana does depart after just one season, but Simone Inzaghi's side will be in the market for a replacement in any case.
According to Foot Mercato, long-serving Tottenham number one Lloris is currently Inter's first pick for a new goalkeeper, despite the fact that the Frenchman is also in the twilight of his career.
Lloris still has another year left to run on his deal at the Tottenham Hotspur Stadium, but the former Lyon man has confirmed that he would be open to an exit this summer after an error-strewn season.
The World Cup winner made four errors directly leading to a goal in the Premier League last season - more than any other player - as Spurs finished eighth in the table with 63 goals conceded.
With Fraser Forster not seen as a long-term successor, Ange Postecoglou has brought in Guglielmo Vicario from Empoli, and there is a consensus that the Italian will immediately cement a starting role for the Lilywhites.
Lloris has returned to Hotspur Way for pre-season training, but the 36-year-old is now said to be in advanced talks over a switch to Inter, despite his public desire to return to boyhood club Nice.
Clubs in Saudi Arabia are also reported to be tracking Lloris, who could supposedly have his waged trebled in the Gulf state, but it is believed that he wants to remain in Europe for the time being.
Since swapping Lyon for North London in 2012, Lloris has been regarded as one of the best goalkeepers in Europe and sits eighth in the club's all-time appearance charts with 447 games.
No non-British player has appeared in more matches for Tottenham than Lloris, who has kept 151 clean sheets for the Lilywhites in that time, including seven from 25 Premier League outings last term.
However, the 36-year-old has not won a single major honour with Spurs, although he was crowned World Cup and Nations League champion with France before calling time on his Bleus career.
Meanwhile, Onana made a significant impact in his debut season with Inter, recording 19 clean sheets from 41 outings across all competitions, winning the Coppa Italia and Supercoppa Italiana to boot.
The ex-Ajax man also kept eight clean sheets en route to the Champions League final, but the Nerazzurri came unstuck in a 1-0 defeat to Manchester City in Istanbul.