Mawson, 23, joined the Swans from Barnsley last summer, helping the club maintain their Premier League status for another season.
With Kevin Wimmer's future in north London uncertain, various reports have suggested Tottenham are on the lookout for another centre-half to provide cover for Toby Alderweireld and Jan Vertonghen this summer. The Sun claim Mauricio Pochettino has already instigated contact with Swansea over Mawson, adding the club will move forward with a £15m (€17.1m) bid for the defender.
Jenkins insists however the club are not looking to cash in on any of their players, particularly, Mawson, who he feels would stand to benefit from remaining in south Wales for the foreseeable future.
"We aren't putting figures on our players," the Swansea chief told BBC Sport. "We see the figures bandied around in the Premier League and they are crazy, but we are part of that. We will do our best to add to the team, not take away from it. We have had no direct contact from any club, it is pure speculation and we hope it remains so."
On Mawson specifically, he said: "There has been no firm interest, but his profile is being raised, we understand that. But we think he's got a few years left with us to develop his career."
Tottenham had been credited with keen interest in Harry Maguire before the 24-year-old signed a five-year deal with Leicester City on Friday for a reported fee of £17m.
Spurs have also been linked with a move for Manchester United defender Chris Smalling. The England international's future at Old Trafford has fallen under further uncertainty following the signing of Victor Lindelof, with the Sweden international expected to form a partnership with Eric Bailly at the heart of Jose Mourinho's defence next season.