Swans chairman Hugh Jenkins said of the 23-year-old winger: "To get him signed and involved before pre-season training will be a big plus for us.
"To get the first player signed is important. We're happy with what we've got but we know we have to add probably three or four players to that.
"Hopefully with the first finalised in the next 24 hours we can finalise the rest between now and the middle of July."
Swansea have ended their interest in Rochdale striker Grant Holt though following the player's decision to sign a new contract.