The former Iceland coach has found himself a shock contender to become the next manager at Tynecastle.
Thordarson, who enjoyed spells with Stoke, Barnsley and Notts County, would jump at the chance to revitalise Hearts and show their rivals Hibs they were wrong not to give him a full-time deal.
The Akranes boss told the Daily Record:"I know quite a lot about Scottish football. I came close to the job at Hibs in 2004 before Mowbray took over.
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."