The England U-21 left back has been linked with a host of Premier League clubs, with Mick McCarthy one of the leading admirers.
Wolves appear unwilling to spend the £500k which would persuade Chelsea to part with one of their young starlets on a season long loan, instead switching their attentions to Hearts defender Lee Wallace.
The Midlands club looked to be Swansea's major challengers in the hunt for Bertrand, but now they have left the chase, it seems to pave the way for Brendan Rodgers to make his move.
Swansea are in the hunt for a left back, with question marks still over the future of wantaway Welsh international Neil Taylor, who is a target for Newcastle United.