McNamara, 39, is currently in charge at Partick Thistle and will be officially unveiled at a Tannadice press conference this afternoon.
Peter Houston, 54, announced earlier this month that he would be leaving United at the end of the season but brought forward his departure and left the club on Monday.
Partick confirmed the approach in a statement on their website which read: "The directors have reluctantly granted permission for Jackie McNamara and (assistant) Simon Donnelly to speak to Dundee United their vacant managerial position."
Former Celtic right-back McNamara is in his second season as Thistle boss - it is his first managerial job - and he has guided them into second place in the First Division this term.
McNamara made 33 appearances for Scotland and also turned out for Dunfermline, Wolves, Aberdeen and Falkirk before ending his playing career with Partick Thistle.
He initially took charge of the Jags on a caretaker basis after the departure of Ian McCall in April 2011 before being appointed full-time a month later on a one-year rolling contract.