United have had three bids for Mount rejected, the latest on Friday worth around £55 million ($69.9m).
Chelsea have indicated they will accept an offer of £58m plus another £7m in add-ons and suggested face-to-face talks in an effort to resolve the situation.
However, United believe their valuation of Mount is fair given the England international only has a year left on his contract and has informed Chelsea of his desire to move to Old Trafford.
Sources have told ESPN that United's latest offer for Mount remains on the table, but enquiries have been about the availability of other targets, including Brighton midfielder Moises Caicedo, Ajax's Mohammed Kudus and Taylor Booth at FC Utrecht.
United are working within a strict budget this summer. As well as a midfielder, manager Erik ten Hag would also like to sign a striker and a goalkeeper.
Uncertainty over David de Gea's future means money might have to be spent on signing an established No. 1 rather than a cheaper option who could provide competition for the Spaniard.
De Gea's contract is set to expire on Friday, and talks over a new deal are described as "open."