But Vukasin Poleksic, the club's goalkeeper, has strongly denied trying to influence the outcome of the match - despite being banned for two years by Uefa for not reporting approaches from match-fixers.
The Hungarian club confirmed Uefa had taken action against Poleksic in 2010 for not reporting approaches from fixers before two European matches - against Liverpool and Fiorentina.
Poleksic was banned for two years but the Uefa charge at the time only specified Fiorentina, and Liverpool say they have never been notified by any organisation that the match at Anfield was under investigation.
Last night the goalkeeper insisted he had not tried to throw the match at Anfield.
"Anyone who watched the match would know that what people are saying is bull," Poleksic said in an interview.
"We lost 1-0 at Liverpool and I played a good game. I made lots of saves: a one-on-one against Albert Riera, one from Fernando Torres, one from Steven Gerrard. I remember it all. How can anyone say I threw the game?
"The match did not seem at all odd that night. There was nothing. I was just delighted to be playing at Anfield. It was a great night for me and my club and we played well."
There has never been any suspicion of wrongdoing by anyone at Liverpool, who won the match in question 1-0.
European enforcement agency Europol said yesterday one Champions League game in England was one of 380 games under investigation, and Debrecen confirmed a report in a Danish newspaper that their games were involved.
A statement on Debrecen's website said: "The disciplinary committee's position was that Vukasin Poleksic neglected his obligations when he didn't report in time that, before two international matches of DVSC, unknown persons attempted to persuade him to influence the outcome of the matches.
"The two matches were the away game against Liverpool and the home encounter with Fiorentina.
"Neither DVSC nor the player wish to react further, all the more so as all the information has been released about this affair during the summer of 2010."
Poleksic bemoaned his failure to report approaches from fixers.
"Every goalkeeper in the world makes mistakes but my big one was that I didn't call the police," he said.
"I didn't play for two years because of this but it's my fault because I didn't report it.
"But I didn't fix anything. I came back in June and the club have been behind me the whole time."
A Liverpool spokesman said: "We have had no contact from Europol or any other organisation over this."
Follow us @SprtNationalUAE