Despite losing their first two group matches, Honduras retain a slim chance of progressing to the last 16 for the first-time in their history when they face Switzerland this evening in Manaus.
However, attention ahead of the fixture has been on Izaguirre's relationship with Suarez after the defender publicly expressed his frustration at being substituted in their last match against Ecuador.
Izaguirre was hauled off at half-time of the 2-1 defeat against the South Americans and, speaking to the press after the match, described himself as "very upset" and "sad" before adding: "I know the coach is in charge, but I am annoyed."
Nevertheless, the left-back, who is expected to start against the Swiss, dismissed suggestions of a breakdown in his relationship with Suarez.
"There is no reason for people to seek problems where there are none," said the 28-year-old.
"I can say with a clear conscience that I have no issues at all with Suarez.
"It was maybe a mistake to be so passionate after the match, but some said I attacked the coach.
"That is not the case, I was just frustrated and showed that after the defeat to Ecuador."
To have a chance of progressing, Honduras must win by at least two clear goals against Switzerland and hope France beat Ecuador.
Even then, they would need to overhaul a goal difference deficit of four to usurp the Ecuadorians.
"The final result against Ecuador was a shame, as we played very well," continued Izaguirre.
"We fought until the last minute and we need to do that again.
"However unlikely, we need to have faith that it is a possibility and try to achieve a great result against Switzerland."
While Izaguirre looks to do the impossible, the Swiss are bidding to erase the frustration of 2010.
Their hopes of reaching the last 16 in South Africa four years ago were dashed as they were held to a goalless draw by the central Americans in their final group game.
The situation is similar this year as they face the same opponents in Manaus looking for a victory to progress from Group E.
A draw would suffice if Ecuador lose to France but, with an inferior goal difference to the South Americans, with whom they are level on three points, the Swiss cannot afford to be too relaxed.
Midfielder Blerim Dzemaili said: "Everyone can nurture big dreams, but first we have to do a little homework and that is to beat Honduras.
"We have seen that the big teams just relying on individuals are quickly eliminated, which little Switzerland can't afford.
"We have to give our all together, like we did against France - but we also had some bad luck after they scored their early goals."
In the group's other game, France will be hoping to round off a stunning start to their campaign with a third-straight win, with them virtually guaranteed to finish top of Group E, with Nigeria the favourites to face them in the last 16.