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The 30-year-old has been on trial at the Magpies, after being released from League One Bradford City in the summer. He had been one of the star performers in last week's friendly 2-0 win over Hucknall Town, giving an assured performance at left back.
The Nottingham-born player is also able to operate at centre back and in midfield, with Thordarson already stating that versatility will be key when he decides who to bring to Meadow Lane this summer.
The Iceman and the club are still keen to bring the former Sheffield Wednesday man to the club, but a move will again be dependant on Armstrong lowering his current wage demands.
Should a deal be struck, Armstrong would join new signings Kevin Pilkington, Lewis McMahon, Brian O'Callaghan and Andy White in Thordarson's new-look Notts County squad.
For all the latest transfer news and gossip, check back to NCM throughout the summer.