Thordarson has been in talks with a number of his players' agents for almost a month with a view to extending their deals and now admits that, for some, a positive solution is not far away.
The County boss has been especially keen to keep David Pipe, Mike Edwards, Julien Baudet and Lee Crooks but is unwillinging to reveal names at this stage.
"The latest news is quite positive," he told the official website.
"It looks as if we are closing-in on a couple of contracts. At the moment it is looking good with two or three of the players that are currently in my squad.
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"The players concerned are those who are very much part of my backbone. It is very vital for me to sort that out. My target is to sign those before I move onto the others."
Thordarson's news comes on the same day that arguably the club's best player, David Pipe, said that he would like to remain at the club.
Pipe has been linked with a number of League One clubs including local rivals Nottingham Forest, but insisted that he is still happy at Meadow Lane.
"It is fair to say there were four or five clubs that showed an interest, but I have been offered a new contract with Notts County and I am happy with that," said the 22-year-old.
"Talks have been going on for the last few weeks and it is all very positive.
"I love the place. The fans have been great to me since day one and I don't see any reason why I shouldn't re-pay that with a bit of loyalty.
"I don't know when I will sign the contract but I am hopeful that it can be sorted soon and then I can look forward to the future."