The Portuguese trainer is under intense pressure to win the love of the Phobian supporters following a slow start as head coach of the club.
Reports in the media suggested that he had been told to win his next five games to save his job.
But Traguil, who is worried about their current performance, has denied those claims.
“No one has told me that I should win my next five matches or leave the club, it is totally false,” he said
“I also heard and read about it, but I have not spoken to any management member or a board member about any ultimatum.”
Sergio Traguil originally joined Hearts as a youth team coach but was elevated to the head coaches position following the departure of Kenichi Yatsuhashi last month.