Like Hreidarsson, Sigurdsson can operate at left-back or in the centre of defence and the 24 year old would require no fee, after leaving Belgian outfit, Racing Genk.
Town boss Jim Magilton told the club site: "Hermann Hreidarsson has played with him for Iceland and spoke highly of him.
"The lad's coming on tour with us and we'll have a look at him over the next week."
Championship side Stoke City were one of a number of clubs tracking him over the last January transfer window and the player is experienced at international level.
The Town boss has made no secret of his desire to strengthen his left-back options with only youngster Scott Barron as recognised as playing in the position, as Matt Richards has adapted his game to midfield and Sito Castro and Fabian Wilnis are predominantly right-sided.
Speculation has recently been linking Dan Harding, the Leeds left-back with a switch to Portman Road, as part of a bargaining tool to convince Jim to part with experienced midfielder Darren Currie. Should Harding join Town in that deal, Sigurdsson's talent as a cover for a centre-back position would need to be strong enough to convince the manager to eat into his allotted wage bill.
Magilton will be taking two trialists on tour with his squad, with midfield holding Frenchman Alexis Bertin still looking to win himself a temporary contract after a couple of impressive performances in the games at Boston and Galway.