That's the claim of the Mail's Dominic King and Paul Joyce in The Times who suggests that Everton will revive their interest in the Icelandic star after failing to land him with a reported £25m bid last summer.
Burnley's Michael Keane, Sunderland's Jordan Pickford and Brazilian striker Willian Josè also continue to be linked.
Swansea were not interested in selling the 27-year-old at that time but the player's own ambitions may force their hand this time. Sigurdsson hinted to the media last month that while he has enjoyed his time with the Swans, he is keen to play for a big club again.
Sigurdsson spent two seasons at Tottenham Hotspur before moving to South Wales in 2014.