Speculation began when the Cobblers revealed they had approached another club in Sky Bet League Two for permission to speak to their manager.
The Oxford Mail understands Northampton have made contact with United about their manager, although neither club would confirm this.
Wilder last night became the clear favourite with bookmakers, his odds tumbling to 1-4.
The situation should become clearer today, with the U’s boss due to give his regular press conference to preview tomorrow’s clash with Torquay United.
Speculation took a twist when Newport County denied being approached by Northampton for Justin Edinburgh yesterday lunchtime, only for the manager to reveal he had turned down interest from the Cobblers.
It is the second time in quick succession that Wilder has been targeted by a League Two rival.
He was given permission to speak with Portsmouth last month and the 46-year-old made it clear a key reason behind the decision was the fact his contract expires at the end of the season.
Andy King has been in charge at Sixfields since Aidy Boothroyd was sacked on December 21, picking up four points from four games.
He is expected to be at the helm for Saturday’s game against Chesterfield, but the Football League’s basement side are keen on making an appointment shortly.