The 20-year-old Dutchman has recently been hailed as one of the nation’s top emerging talents after establishing himself in the Amsterdam outfit’s first-team squad.
Due to his fine fledgling displays, the Eredivisie giants are keen to tie him down to a new contract, but so far negotiations have been unsuccessful.
It is believed that the youngster’s personal demands are considered to be unreasonable by Ajax, which has prevented an agreement from being reached.
This has alerted United, with manager David Moyes thought to be ready to take advantage of the situation.
The Scot is desperate to add talented players to his ranks next month, with a new centre-back a priority.
Scouts from the Red Devils have been impressed by the defender’s displays, and are believed to be sure that he would jump at the chance to move to Old Trafford.
Ajax may be open to selling form around £5m, and United could further sweeten the deal by allowing Denswil to return to the Amsterdam ArenA on loan for the remainder of the season.