Izaguirre, 30, joined Celtic from Motagua in his native Honduras in the summer of 2010, having impressed at the World Cup in South Africa.
Celtic's Emilio Izaguirre
The left back has now racked up a huge 250 appearances for Celtic, becoming one of the Bhoys' most dependable players during almost seven years in Glasgow.
Over the last 18 months, Izaguirre has been forced to deal with being second-choice behind talented youngster Kieran Tierney, but has filled in admirably during Tierney's recent injury lay-off.
Celtic's Emilio Izaguirre during training
That has prompted talk of Izaguirre earning a new contract, given that his current deal expires at the end of the season, but The Scottish Sun now report that Leeds United and Sheffield Wednesday are keen to lure him to England.
Leeds have a star left back in the ranks with Charlie Taylor impressing, but he's out of contract in the summer, and manager Garry Monk may look to bring in an experienced left back to help Taylor and youngster Tyler Denton, with Izaguirre fitting the bill whether on the cheap this month or on a free in the summer.
Meanwhile, Wednesday have been forced to use Adam Reach at left back this term, with Daniel Pudil injured and Urby Emanuelson has yet to appear since joining the club, meaning Carlos Carvalhal could look to sign another left back.
At 30, Izaguirre has great experience but also still has plenty to offer, and he may fancy the chance to impress in England, rather than continue as Tierney's backup at Celtic – but the Bhoys should still make a move to keep him in Glasgow and away from the two Yorkshire sides
Would you like to see Leeds or Sheffield Wednesday sign Izaguirre?