Hamllton Academicals were approached by the Welsh side for permission to speak to Billy Reid, but the coach wanted to stay with the Scottish Premier League side.
Huw Jenkins, the Swans chairman, said they have approached two other clubs but would not say who.
Simon Grayson, the Leeds United manager, has signed a contract extension to stay at Elland Road for a further three years.
Grayson, 40, took charge of the Yorkshire side in December 2008 and secured runners-up spot in League One last season.
My intentions have always been to take the club forward and after achieving promotion last season, I hope we can go on to fulfil everyone's dream of winning promotion back to the Premier League," he told the club's official website.
"I work closely with the chairman [Ken Bates] and [chief executive] Shaun Harvey, we've got a good relationship and I hope we can keep progressing as a club. That's what we're all working towards."
Hull City have signed the midfielders Nolberto Solano and James Harper, both on free transfers.
Solano, 35, was expected to retire after being released by Leicester but has been reunited with his former Foxes boss Nigel Pearson at the KC Stadium.
Harper was released by Newcastle United following their promotion back to the Premier League.
Adam Pearson, head of operations, has said the club will need to sell at least two more players after Jimmy Bullard's loan move to the Scottish Premier League side Celtic collapsed on Monday.
Millwall have taken midfielder Darren Carter on trial from Preston North End. The midfielder, 26, is training with the Lions as they consider a six-month loan.