Starsport understands Pochettino wants to lure the Swansea ace back to White Hart Lane in the belief he is a better and cheaper alternative to long-time target Ross Barkley.
Spurs have been keeping close tabs on the England and Everton midfielder all season and were expected to make a bid this summer.
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But Pochettino knows the Toffees want around £50m for the midfielder and is reluctant to meet the asking price, particularly with the club also facing the expense of rebuilding White Hart Lane.
Sigurdsson moved from White Hart Lane to Swansea in the summer of 2014, not long after Pochettino had taken over as boss.
He was not consulted about the decision and revealed earlier this season that he thought the transfer had been a big mistake.
Spurs chairman Daniel Levy is willing to sanction a move for Sigurdsson, even if it makes them look foolish for selling him.
The situation is similar to the one Manchester United find themselves in as they look to re-sign Michael Keane.
United boss Jose Mourinho is willing to pay Burnley £25m for Keane – even though the club sold him for just £2m in 2015.
Sigurdsson has been one of the most consistent and impressive midfielders in the Premier League this season.
Toffees boss Ronald Koeman is a huge admirer and was plotting a bid for him himself this summer.
He had the 27-year-old lined up to replace Barkley, who has failed to meet his deadline to sign a new deal at Goodison Park.
Pochettino remains a big fan of Barkley, but knows he is far from the finished article and that Sigurdsson has more proven experience at the highest level as well as knowing Spurs inside out.
The Icelandic international made 58 league appearances for the London club between 2012 and 2014 and remains popular with fans.
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