Town chairman Dean Hoyle has rejected two bids from the Rams and insists the former Middlesbrough and Norwich midfielder is not for sale.
Butterfield rifled home an unstoppable left-footed drive from the tightest of angles to end Brighton’s perfect start to the season.
Huddersfield’s squad was under the microscope with goalkeeper Alex Smithies on the brink of a £2 million move to QPR and Derby testing Hoyle’s resolve over Butterfield.
And they were shaken after just 17 seconds when Beram Kayal smashed home from the edge of the box straight from the kick-off.
It was only in the second half that the 25-year-old got Huddersfield going, levelling in the 54th minute.
Brighton keeper David Stockdale pulled off a superb save from Nahki Wells and Butterfield again five minutes from time.
Huddersfield boss Chris Powell said Butterfield was integral to his squad and wanted him to stay.
Powell admitted his players were “rocked” by the early goal and said: “I can’t tell you how hard that is.
“The goal rocked us in the first period and everyone was stunned. We couldn’t get ourselves going and we needed half-time.
“Half-time came and I got into the players in a positive way and the players were exceptional. The effort, character and commitment they showed was magnificent.”
Powell said he felt his side deserved all three points for the second half show but added: “We are a work in progress. We have a few new players and we showed here what we showed last season, that we have to play to our maximum.
“Other teams have spent some money and we know we are in no position to do that.”
Brighton boss Chris Hughton was happy with seven points from three games and said: “If you had said that to me at the start of the season, with two of the three games away from home, I would have been delighted.
“We couldn’t have made a better start to the game and it was one of those strikes that as soon as he hit it you knew it was going in.
“There were too many occasions when the first pass went astray. Overall a draw was a fair result but the best two chances of the game fell to us. We started well and looked resilient.
“You cannot control a game for the whole 90 minutes, especially away from home, but we needed more control than we had. Still, it was a good point and we go again and try to win the next game.”