The deal is rumoured to be worth around £5m plus striker James Vaughan.
Canaries boss Chris Hughton is keen to add to his defensive options and it seems the Honduras international is the man who fits the bill. The 26-year-old could be in line to take over from current left-back Marc Tierney.
Izaguirre has impressed since signing for the Scottish giants in 2010 and was linked with a move to Manchester United last summer.
Norwich are hoping that Neil Lennon's long-standing admiration for Vaughan could help move the deal along.
Izaguirre has reportedly become disillusioned with life in the Scottish Premier League following the demise of Rangers.