Liverpool's search for a new manager is due to end this week with an announcement expected on Friday.
Roberto Martinez and Brendan Rodgers have been the two main candidates throughout the two-week process of whittling down potential contenders and Press Association Sport understands an announcement will be made on Friday.
Both Martinez and Rodgers returned to Britain in the last 24 hours after trips across the Atlantic but only the former had spoken to Reds principal owner John Henry, interrupting a holiday in Barbados to fly to Miami for brief talks.
Rodgers along with his wife, was a guest of the Football Association of Wales for Sunday's friendly against Mexico in New Jersey.
The Northern Irishman met with chairman Huw Jenkins on Tuesday but the club insist it was a scheduled appointment and he had not cut short his trip to America especially for it.
Swansea stress they have received no second approach from Liverpool - Rodgers having turned down their initial advances almost a fortnight ago - and PA Sport understands the pair did not even discuss the Anfield vacancy at their meeting.
The primary topic of conversation appears to have been transfers, with the Swans on the verge of completing a club-record £6.8million transfer for on-loan Hoffenheim midfielder Gylfi Sigurdsson and interested in a loan deal for Tottenham's out-of-favour Giovani dos Santos - whom Rodgers watched in New York.
However, despite suggestions elsewhere that Rodgers had already been offered the Liverpool job the club refused to comment officially on their manager's position.
Yesterday 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.
It read: "We would like to clarify the speculation in the press surrounding our manager Brendan Rodgers.
"We would like to confirm that there has been no contact from Liverpool and nothing has changed since our previous statement on the issue."
On 18 May the south Wales club had said: "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."
Yesterday's statement did little to quash speculation and overnight bookmakers moved Rodgers ahead of Martinez, who flew into Manchester Airport this morning from the Caribbean to be confronted by a television camera crew and photographers but left without commenting.
The Spaniard has been given a deadline of Thursday by Latics chairman Dave Whelan to decide his future.
But he touched down in England to reports suggesting Rodgers was now in the driving seat despite having turned down Liverpool first time around because, it was suggested, he did not want to become involved in a lengthy process with up to 12 names mentioned at the time.
There have been growing murmurings in Wales and his native Northern Ireland that Rodgers would now be more receptive to the Reds with the list of candidates having been whittled down.