Thordarson has publicly stated that he wants three players to bolster his team's playoff push - with the arrival of at least two strikers and a midfielder on the manager's wishlist.
But, if he is unable to do this, it won't be through lack of trying...
One man who's already walked through the exit door, of course, is Glynn Hurst.
The Magpies top-scorer requested that his contract be terminated to allow him to join Shrewsbury Town on an 18-month deal. With Hurst and Thordarson suffering an uneasy relationship, the County boss opted to let his nine-goal striker leave in order to fund new signings.
With the 29-year-old one of the higher earners at Meadow Lane, his wages are expected to be spent on two new players, who may well be signed in time for Saturday's visit of Darlington.
While Hurst's exit is the only immediate one, Thordarson currently has four other Mills-signed high-earners in his existing squad on the transfer list that he hopes to move-on to allow him to bring-in further new faces.
Matthew Williams is a graduate of the Manchester United academy but has spent the entire season out-of-favour and available for free transfer.
The 23-year-old forward has made just two appearences for County all season and, though the possibility of a permanent move to another league club seems unlikely, a loan move with the Magpies paying a sizeable chunk of his wages could suit all parties.
The other two outcasts currently at the club are Matthew Gill and Gavin Gordon (left).
After securing regular starting places last season, both have been relegated to cameo roles under the Icelandic boss, making 21 appearences between them this season.
Gordon has remained available for the past two months, while Gill was transfer-listed shortly before Christmas.
New arrivals are expected - with or without the duo's departure - so Thordarson believes it would be in the best interest of the players to move on, with Gordon keen to secure a move back to former club Lincoln City.
Gill meanwhile, will be hopeful of attracting interest from other League Two clubs, after clocking-up an impressive 50 first-team appearences last season.
The other possible exit is that of star defender Kelvin Wilson. Out of contract at the end of the season, the omission of Wilson from the past two league games due to injury has set tongues wagging among the Notts faithful that he is destined for the exit door.
Widely expected to leave the club in the summer, Thordarson could opt to cash-in on the highly-rated 20-year-old now, rather than risk the often-unreliable tribunal system.
If you think those predictions are wide of the mark, what about the return of the man Notts fans loved to hate, Darren Caskey?
Caskey is thought to be keen on a move back to English football after recent time spent in the USA, with his infamous waist-line thought to be heavilly trimmed and back to a manageable amount.
But surely we're not going to see HIM again, are we?
Of the more realistic possibilities, talk was rife among home support at Monday's clash with Barnet that Boston's Jason Lee (below) is set for a move to the 'Lane.
A striker very much in the same mould as the much-mallinged duo of Andy White and Gordon, talk of Lee's possible arrival hasn't exactly gone down well with all Magpies fans.
Of course, the 34-year-old enjoyed a spell at Nottingham Forest in the mid 90's, something that won't help immediately endear him to the County faithful.
He did impress in Notts' 1-1 draw with the Pilgrims earlier in the campaign though, scoring his side's goal.
With Thordarson playing his cards very close to his chest, the rumour mill has churned out numerous other names, with seemingly nothing more than circumstantial evidence linking them to a move to the Magpies.
Lee Peacock is another striker that has been strongly touted. The Sheffield Wednesday man has managed just three goals for the struggling Championship side all season and has been told he is surplus to requirements by manager Paul Sturrock.
That said, it would be a major coup should Thordarson manage to bring in a man - still only 29 - who has commanded over £1million in transfer fees over his career, to Meadow Lane.
A more likely target of Thordarson's is the much-travelled Tony Thorpe. The 31-year-old striker has scored goals for all of his eight professional clubs and carries the clout and the reputation neccesary to replace Hurst.
Currently without a club after a short spell at Swindon, Thorpe has recently been training with Wrexham but, having been born in Leicester, the Magpies carry the geographical advantage, if little else, in the bid to secure the striker's signature.
Allan Borgvardt (right) is one player who has been a much-touted name ever since Thordarson was appointed. A Danish striker who has set the premier Icelandic division alight, the 24-year-old has been widely-tipped for a move to England for some time.
While the prospect of signing Borgvardt remains unlikely, Thordarson has already raided his home nation once, with the County boss looking at bringing in Andri Steinn Birgisson, as earlier revealed on NCM.
The international midfielder spent time on-trial at Meadow Lane earlier in the campaign and Thordarson is considering offering the 22-year-old a permanent contract at the club.
And, if you want to be really lazy, why not link him to his son, too? Despite a change of manager in the summer, Toddi Gudjonssen remains hugely out-of-favour at Stoke City and a cheeky loan bid could be in order.
When you add to all of the above, the probable offer of permanent contracts to non-contract duo Adam Tann (defender) and Liam Needham (midfielder), it proves that Thordarson wasn't lying when he stated that he expected this to be a busy period for the Magpies.
With all of this speculation, we can't wait.
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