Hull boss Phil Brown will hold talks with Daryl Murphy later this week after the Tigers agreed a fee with Sunderland for the Republic of Ireland striker.
Murphy has been deemed surplus to requirements at the Stadium of Light by new manager Steve Bruce and looks set to become Hull's first signing of the summer.
The 26-year-old still needs to agree personal terms and undergo a medical but Brown is optimistic the deal can be concluded as he told the Hull Daily Mail: "It's advanced and we've spoken to Sunderland and agreed terms. Hopefully in the next 48 hours it might progress to a stage where we can complete a medical."
He added: "It's an initial fee of £1.5m building up to £2.5m that has been agreed and I hope to meet with him on Thursday.
"Hopefully by then we'll have progressed it further."
Hull are also chasing Cardiff duo Joe Ledley and Ross McCormack but the clubs are some way apart in their valuations of the 22-year-olds.
"Where Ross McCormack and Joe Ledley are concerned, you're looking at players who have done very, very well at Cardiff in the Championship," added Brown.
"Yes they would interest us but not at the prices that are being quoted. Until those prices are brought down, if there is such a price, we're not interested.
"It is difficult when players want to move from a selling club and agents think they can progress them quickly."