The 26-year-old has attracted interest from Paul Clement's side and Burnley this summer, with the Clarets having their own bid rejected earlier this month.
Clucas was not part of the matchday squad for Hull's trip to QPR on Saturday, forcing him to insist on Twitter that he was not on strike.
New Hull boss Leonid Slutsky confirmed after the game at Loftus road that Clucas was poised to "another club".
"I don't know [which club] but it's Premier League. I think there will be official information, it's his decision. I only listen to information - I don't take part in negotiations. I think a deal will be in some days."
Swansea are now expected to complete the signing of the Englishman within the next two days.