The Scottish Sun says the Ireland legend visited Istanbul, spending 48 hours in talks with the club about their ambition and viewing training facilities and the city.
He was also happy with the £1.6million-per-year contract offer and his keenness to return to football made the move to Turkey appetising to him.
But he refused to make a decision until he returned to England to speak with his wife Theresa, who was reluctant to move.
Kasimpasa vice-president Hasan Hilmi revealed: "He is not coming because of his wife and children. There is nothing we can do, there are no alternatives."