After speculation throughout the summer, the Icelandic attacking midfielder looks set to sign a five year deal with the move expected to be concluded in time for the player to face Manchester City this weekend.
Sigurdsson was the Swans best player last season, contributing nine goals and 13 assists with his departure expected to set off a domino effect in the transfer market.
The Sun report Wilfried Bony could make a return to the Liberty Stadium as Paul Clement looks to splash some of the cash from Sigurdsson's departure.
The Ivorian striker would cost the Swans around £14m from Manchester City and compete with Fernando Llorente and new arrival Tammy Abraham to start up front for the Welsh club.
Bony, who left the Liberty Stadium for the Etihad Stadium in 2015 for £28m, spent last season on loan at Stoke City but only managed two goals in 10 appearances there - both of which came against the Swans.
Elsewhere Southampton FC have lined up Lazio defender Wesley Hoedt - but not as a replacement for Virgil van Dijk.
The 23-year-old Dutch centre back was attracting interest from Leicester City and West Ham United but it is the Saints that are close to competing a £15.4 million deal according to The Mirror .
Hoedt would be the second centre back Southampton have signed this summer - after the arrival of Poland international Jan Bednarek - but chairman Ralph Krueger insisted that does not mean van Dijk can leave.
The want away defender handed in a transfer request 10 days ago but club captain Steven Davis said he would be welcomed back with "open arms" reports the Mail Online .
And finally, speculation has increased Manchester United are about to complete a swoop for Inter Milan winger Ivan Perisic.
The Express has reported a crucial clue could be found in the shirt numbers announced by United this week - Andreas Pereira will no longer wear number 44 on his back - the shirt favoured by Perisic.
The announcement has fuelled rumours United are willing to meet the £48m asking price set by Inter and land Jose Mourinho's fourth - and probably final - target of the summer.