The Sun says Dinamo Zagreb vice-chairman Zdravko Mamic jetted into Tyneside on Tuesday and met Toon officials in a hotel to discuss the move.
But Geordies executive director of football Dennis Wise has won the battle.
A source close to Modric said: "Mamic came back to Croatia and insisted that Luca is close to moving to Newcastle.
"He always talked about Spain but Portsmouth's Croatian star Niko Kranjcar has told him to move to England.
"The money Newcastle are offering is fantastic."