The club have denied suggestions in some quarters that Rodgers cut short a trip to New York in order to return home to talk to the chairman after rumours began to surface of the Reds' renewed interest.
Rodgers, along with his wife, was a guest of the Football Association of Wales for Sunday's friendly against Mexico at the MetLife Stadium in New Jersey.
Press Association Sport understands Rodgers is speaking with Jenkins on Tuesday afternoon but that the meeting is not as a direct result of new speculation about the 39-year-old.
Liverpool's apparent interest will no doubt be discussed at their get-together but as yet Swansea say there has been no approach from the Merseysiders since they were turned down a fortnight ago.
On Monday, Jenkins dismissed the Reds' renewed interest as "pure speculation" and the club issued a statement to stress their position had not changed from two weeks ago, when Rodgers turned down the chance to speak to Liverpool.
"We would like to clarify the speculation in the press surrounding our manager Brendan Rodgers," the statement read.
"We would like to confirm that there has been no contact from Liverpool and nothing has changed since our previous statement on the issue."
However, the statement did little to quash speculation and overnight Rodgers moved ahead of Wigan's Roberto Martinez as the bookmakers' favourite.
It is believed Rodgers initially turned down Liverpool as he did not want to become involved in a lengthy process, with up to 12 names being linked with the post at the time.
But there is growing belief in Wales and his native Northern Ireland that he would now be more receptive to an approach with the list of candidates having been whittled down.