Newspaper reports alleged Poll made the remarks and suggested he told Chelsea: "Your discipline is out of order"
Poll booked six Chelsea players and sent off John Terry in the 2-1 defeat.
Hackett told Five Live Breakfast: "I have very serious doubts that one of our most experienced and world-class refs would make that kind of comment."
He said: "It is disappointing. It puts doubt in the public's mind about the integrity of one of my referees but it will be investigated."
Hackett, head of the Professional Game
Match Officials Board, also revealed that all the officials were on open microphones - and his initial inquiries led him to believe Poll had not made the comments.
He added: "The player who has made the comments should be aware that the referee, along with his assistant referees, were all wearing microphones.
"My assessor can hear from before kick-off to the end what is being said. If anything untoward was said I will be able to discuss it with Graham's colleagues on the day.
"Already having spoken to one of his colleagues, who was listening, it has been flatly denied.
"I have told Graham not to comment on this matter because it may be investigated by the football authorities."
Chelsea boss Jose Mourinho and his players were unhappy with Poll's handling of the defeat at White Hart Lane. The Blues went 1-0 up before losing 2-1. And Chelsea defender Ashley Cole said: "With my booking, I said to him, 'I'm more than 10 yards. Why should I go back if I am more than 10 yards?'
"And he said, 'Because I said so.' I said, 'But I' m more than 10 yards', and that was it. Yellow card. No warning or explanation.
"I'm not moaning, I'm really not but we really shouldn't lose a game like that.
"Once again we scored a goal that was fine. I've seen it on TV and once again the referee has robbed us again because if we had gone to 2-0 then the game would have been dead."
Cole believes that Chelsea, like his previous club Arsenal, are now being singled out by referees because of their success.
He added: "When I was at Arsenal and we started to win things, the referees started to question our discipline and give us yellow cards. I have come to Chelsea and it's exactly the same.
"It's definitely to do with the team that's winning most. Chelsea are not a dirty team. It's crazy. We have to stick together, put this game behind us, look forward to the next one and win it."