The Wales international spent last season on loan with Swans' rivals Cardiff City, where he scored seven goals and provided 12 assists in 38 appearances.
Steve Cooper went in pursuit of Wilson last summer but was beaten to his signature by the Bluebirds, who were prepared to pay more than the Swans for his services.
However, The Sun reports that last season's playoff finalists remain keen on Wilson and will return to the table in their attempts to bring the 24-year-old to the Liberty Stadium.
Swansea have released a big-earner in Andre Ayew, which is believed to have opened up some funds for new signings, and it appears that Liverpool are reluctant to allow Wilson to leave Anfield permanently this summer.
Wilson's most successful campaign in front of goal came during the 2018-19 season when he scored 18 goals and registered six assists for Frank Lampard's Derby County side. body check tags ::