Southampton are ready to splash the cash this summer.
Sigurdsson has helped keep Swansea afloat this season but the Wales club are still in a relegation battle and could well go down.
That would give Saints leverage in making a swoop for the playmaker who has nine goals and 11 assists this season.
Another target that has emerged for Saints is Leeds United defender Jansson.
The Swede is seen as a potential replacement for Virgil van Dijk.