Having finished as runners-up in qualification Group E, Iceland are a two-legged play-off away from a place in Brazil next summer.
Croatia stand between them and a piece of history, with there a possibility that they will become the smallest nation to ever reach football's showpiece event.
A population of just 320,000 hope that will be the case, and Gudjohnsen is the man expected to lead the charge.
The former Chelsea and Barcelona striker is experienced enough to handle the pressure and admits guiding his country to a major international tournament would represent a new high in his distinguished career.
Gudjohnsen said in the Daily Mirror: "Going to represent Iceland in a World Cup in Brazil would have to be as big a feeling as winning the titles at Chelsea - and I don't say that lightly.
"They were fantastic achievements and gave great satisfaction. It would just be a different sensation. Winning the league, a title, is unique and special but it would be in the same bracket.
"Getting there would be a victory of sorts anyway and I'll see how I feel if we do it, it's hard to imagine.
"When I was at Chelsea and Barcelona you had team-mates going off to the big tournaments while you stayed.
"And at the time the Champions League was for me the biggest and most exciting thing, together with the domestic title - but there is still a chance of a World Cup."
Gudjohnsen, who is now 35 years of age and on the books of Club Bruges, added: "Football is a team game but of course it's nice to have things to reflect on at the end of your career.
"And getting to this World Cup with my home country and all the things and countries we're up against would be incredible.
"It would just be an amazing feat and something unforgettable to be part of. It has always been a distant dream, it has never gone away, however unlikely. Any boy who watches the World Cup dreams about playing in it one day.
"I've been realistic about it in recent years and accepted maybe it would never happen.
"I've always been picked out at home as one of the players who has played for top clubs and won things never to have made a World Cup or major finals."