The Newcastle Jets are awaiting an answer today from former Manchester United star Dwight Yorke on a six-month deal to become the club's marquee player.
"Yes, we are talking to Dwight and hope to have an answer in the next 24 hours," Constantine told The Herald.
Constantine would not reveal the details of the offer, but it is understood the deal would be for the rest of this season and the Jets' Asian Champions League campaign.
Joel Griffiths assumes marquee status from the start of the 2009-10 A-League season.
Jets high-performance manager Ian Crook worked with Yorke at Sydney and has been carrying out negotiations. The Jets have been without a marquee player since the return to Ecuador of Edmundo Zura on November 2.
In the past, Constantine had been against signing a top-end marquee player. But the Jets' journey into Asia and the $20 million on offer in prizemoney has resulted in a backflip.
Regarded as one of the world's premier strikers in his prime, Yorke, 37, has played predominantly in midfield for Sunderland.
He left Sydney FC for the Black Cats on a $500,000 transfer in 2006, reuniting with former Manchester United teammate and Sunderland manager Roy Keane.