Sky Sports sources understand that Bolton have turned down a £5million offer for Mark Davies from Swansea.
New Swans manager Michael Laudrup confirmed earlier in the week that he was hoping to bring in further reinforcements before the transfer window slams shut.
Laudrup has also admitted it would be vital to sign a replacement if a regular starter leaves, amid speculation continuing to link Joe Allen with a move from Swansea to Liverpool.
Davies has been identified as somebody who could strengthen their midfield and an approach is thought to have been made to Bolton.
However, the Trotters are believed to have rejected the bid as they aim to hold on to Davies ahead of the new Championship season.
Owen Coyle has made it clear that he will fight to keep his best players despite suffering relegation from the Premier League at the end of last season.
Swansea will now have to decide whether to return with an improved proposal or turn their focus to other targets.