The former Iceland coach has found himself a shock contender to become the next manager at Tynecastle.
I was offered the job and it was a discussion to take over until the end of the season.
"I wanted the job long-term but they just wanted me to take the team to the end of the season and then make a decision.
"I don't need a trial period. They don't know what I stand for and what I have done in the game. I have been a manager for 22 years and I am not just jumping into it.
"You can never tell but I am sure I'd have done a good job. If you look at what they have achieved since I could have done as well as the other managers. Mowbray did well but so could I have."
Thordarson says Hearts should be playing in Europe every season and pushing the Old Firm.
He said: "Hearts are Scotland's third biggest club. It is a shame to see where they are right now. In reality you have the two big teams chasing silverware but you should give them a fair challenge.
"It hasn't been a healthy season for Hearts but I'd never hide. I wouldn't listen if someone said, 'don't go there'. I have always accepted a challenge."
But Akranes general manager Thordur Gudjonssen has issued a "hands-off" warning to Hearts.
He said: "Gudjon is a key figure in our club and we are not keen to let him go."