Both clubs have had bids rejected for the 28-year-old, who scored in a 3-1 win at York City on Saturday, and Wycombe are not willing to accept a penny less than their asking price.
The League Two side are demanding in excess of £350,000 for their star striker, leaving the Lions' £200,000 bid well short.
A national newspaper report on Monday morning claimed the Lions had won the race for Beavon's signature, but NewsAtDen understands that this is not the case.
Preston, meanwhile, have walked away from negotiations after upping their offer to £250,000.
Lillywhites manager Graham Westley said: "We've made no secret we've made a bid for Beavon, it's been turned down and the demands on the table are not what we're going to be able to meet.
"It's looking as though the distance between us and them is going to be hard to bridge."
Wycombe boss Gary Waddock has called on clubs interested in Beavon to put up or shut up after months of speculation – fuelled by Preston's public pursuit of the forward in recent weeks.
He told the Buckinghamshire Advertiser: "If you've got a big asset you've got to match the asking price the club wants. Until any club matches that figure, Beavon will be staying here.
"Everybody deals with it in their own particular way. If clubs want to go public with players that they are after, so be it, but we don't. We do it in a different manner."