Talks with Onana's representatives, which started last week, have been productive and United are ready to test Inter's resolve with a package of around €39m plus add-ons.
Sources told ESPN that Inter's valuation is more than €50m but there is hope that a compromise can be reached.
The Serie A side are aware of Onana's desire to move to Old Trafford, where he would be reunited with his former Ajax manager Erik ten Hag.
Ten Hag has identified the Cameroon international as his preferred target as he looks for a new goalkeeper this summer.
Sources told ESPN that United are still pursuing face-to-face talks with David de Gea about his contract situation. De Gea's deal expired on June 30 and he is now a free agent.
Sources told ESPN that Forest want to sign Henderson in a permanent deal and, as things stand, the 26-year-old is unlikely to be part of United's squad for the preseason tour of the United States, which begins in New York on July 20.
Henderson has two years left on his contract but is determined to find regular first-team football in an effort to win back his place in the England squad.
Tom Heaton, 37, is the only other senior goalkeeper at United after his contract was extended by a year at the end of last season.
Mount will wear the No.7 at Old Trafford after being offered the iconic shirt by Ten Hag during negotiations with the club.
ESPN originally said the deal currency was in pounds; it's been corrected to euros.