The Wales international has been the first-choice left-back at the Liberty Stadium for the past two seasons and new Spurs head coach Mauricio Pochettino to keen to make him his first signing at White Hart Lane.
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"There's a lot of speculation about Ben at the moment, as there is with a lot of players at this time of year," Jenkins told the South Wales Evening Post.
"There was an initial interest from Tottenham, but there has been nothing since."
Swansea want Sigurdsson, most probably on loan, included in the deal but new manager Mauricio Pochettino is understood to not yet be ready to sanction the midfielder’s departure with pre-season only recently underway.
Jenkins has again confirmed Sigurdsson has been involved in the negotiations and is keen on bringing the player back to the Liberty Stadium after impressing on loan in 2012.
"Gylfi was put to us and he is one of a number of players we have been speaking about," Jenkins added.