The former Swansea midfielder could be set for a return to the Liberty Stadium this summer, but Crystal Palace are also keen on the £10 million-rated playmaker, according to The Sun.
Pochettino is ready to rebuild the Spurs squad and has already seen Jake Livermore leave to join Hull City on a permanent basis.
The Argentine is not thought to be an admirer of Sigurdsson and will look to make him the next man to leave the North London club.
Sigurdsson joined Spurs in July 2012 as Andre Villas-Boas' first signing but has failed to nail down a regular starting role in his two seasons with the club.
He only made 22 appearances in the Premier League last season and will be a much more important player with a switch to The Eagles or a return to The Swans.
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The Icelandic international scored five goals in the Premier League last season but didn't register an assist.
He recorded an average passing accuracy of 84% but has not been the same threat as Spurs as he was during his loan spell at Swansea in 2012.
This is largely down to the fact that he has been played on the left of midfield and has been unable to produce the long-range shots and through balls he did whilst with The Swans.
A move to another Premier League club would see Sigurdsson play a more prominent role though he will cost around £10 million.