The Icelandic midfielder was on target as Reading, then in the Championship, toppled Liverpool in a third round replay at Anfield in the 2010 competition.
Gylfi also scored winning goals in the fourth round at Burnley and fifth round at West Brom as the Royals made it to the quarter-finals, where they were eventually beaten at Villa Park.
Currently 11th in League One, Coventry arrive at the Lane for Saturday’s third round clash in fine form, a run of 10 matches unbeaten in all competitions ended by Shrewsbury on New Year’s Day.
They’ve lost just six in 25 since the appointment of former Manchester United striker Mark Robins as manager in September and have impressive away form in League One, with seven wins already on their travels.
As Gylfi points out, the Sky Blues are bound to rise to the challenge at White Hart Lane.
“It’s a great occasion for them,” said Gylfi.
“They come up against a top Premier League side and they will come here, want to do a job and take the chance to impress everyone.
“We have to make sure we’re ready for that and we’re in the draw for the next round.”
Gylfi started our New Year’s Day win against Reading and said patience was key as we recovered from the visitors taking the lead in the fourth minute to run out 3-1 winners.
“Reading scored the goal early and that made it difficult for us,” said Gylfi.
“We had lots of shots from outside the box as it was quite difficult to get into positions up against the goalkeeper.
“But sometimes you have to be patient and we know we’ll eventually get those chances, especially playing at home, with the players we’ve got here.
“We had to keep going, keep believing and we got there in the end. The win was well deserved.”