Everton's pursuit of the Iceland international has been going on all summer but there is still no resolution and, with that in mind, boss Paul Clement has opted to leave him out of the squad that will travel to St Mary's.
Fernando Llorente will also miss out after fracturing his arm while on a cycling holiday last month, joining Nathan Dyer (Achilles) and Ki Sung-yueng (knee) on the sidelines.
England Under-21 striker Tammy Abraham is in line to make his debut after securing a season-long loan move to the Liberty Stadium from Chelsea.
Roque Mesa, an £11million signing from Las Palmas, is also likely to see some action in midfield, but goalkeeper Erwin Mulder may have to wait for his Swans bow.
Provisional squad: Fabianski, Naughton, Fernandez, Mawson, Olsson, Britton, Carroll, Fer, Ayew, Routledge, Abraham, Nordfeldt, Mulder, Rangel, Kingsley, Van der Hoorn, Bartley, Mesa, Fulton, Grimes, Narsingh, McBurnie.