The executive vice-chairman was caught uttering something in the direction of Red Devils' defender Jones in the stands during Sky Sports' broadcast of the 2-0 loss at the London Stadium on September 22.
The interaction came after the centre-back - who was sitting behind Woodward during the match - was shown seemingly muttering something under his breath.
However, Woodward has denied those claims and insisted that he was talking to United's club secretary Rebecca Britain - sitting next to Jones - about an incident in the game.
"Phil was talking about whether decisions were offside or not," he explained in an interview with club fanzine United We Stand.
"There was a foul and I turned around to Rebecca Britain, our club secretary [and said] 'Was that a yellow card on him? [Issa] Diop?'"