The Icelander was interviewed for the position at the Walkers Stadium last season before the job was given to Levein, while his son, Joey Gudjohnsen, is a key player for the struggling Championship side.
The County boss has enjoyed a hugely successful management career but has never managed at Championship level or above.
"I am fully committed and just want to focus on our next game," said the 50-year-old.
Thordarson is currently the bookies second favourite for the position with odds of 4/1, but the Foxes board are thought to favour a move for Burnley manager Steve Cotterill, who has received a surge of bets to leave him as the 2/1 favourite.
The Magpies board would be strongly opposed to any approach for Thordarson - who has two and a half years left to run on his current deal - but Chairman Steve Thompson has admitted there would be little point in denying the former Stoke City boss the chance to speak to the Foxes.
Notts are currently enjoying their best spell of the season, losing just one of their last six games to leave them outside the playoff positions on goal difference.
For all the latest on this story, be sure to check back to NCM.