Although Rodgers had previously stated his intention to remain with the Swans, having already turned down the chance to speak with Liverpool, it appears the Reds have not given up on the hope of talking to the Northern Irishman.
Reports have suggested the Reds are set to contact him this week but Jenkins told BBC Sport that was just "pure speculation".
Ten days ago Swansea released a statement confirming they had received an official approach from Liverpool to speak with Rodgers.
"The club is pleased to confirm that Brendan has declined the current opportunity to speak to the Anfield club about the vacant position," it said.
"The Swansea manager is currently working hard to strengthen the squad in readiness for the new Barclays Premier League campaign."
Wigan's Roberto Martinez is still seen as the front-runner, having held talks with Liverpool's principal owner John Henry in Miami last week.
The Spaniard is due back from a Caribbean holiday on Tuesday but despite his suggestion over the weekend he would hold a press conference at which he would outline his future plans, no such arrangements have yet been made.