Grimsby, second from bottom of the Football League, sacked manager Mike Newell on Monday following Saturday's fourth successive league defeat and Windass wants to bounce straight back into management after being shown the door at fellow strugglers Darlington last month.
Windass, 40, said: "I have applied for the job at Grimsby. The fact I've just retired as a player was purely coincidental, but this is too good an opportunity for me to let it pass by.
"I was disappointed not to get the chance at Darlington when (manager) Colin (Todd) left and I've always said I wanted to be a manager, to make my own decisions and be my own man. I've said that for many years now.
"Grimsby would be a great club for me to start my managerial career and I believe I've got the hunger and attributes to make a real success of it."
Windass, a former player with hometown club Hull, Bradford and Middlesbrough among others, officially quit as a player on
Monday. He played his last league game as player/coach for Darlington in a 2-0 home defeat to Bournemouth in September before both he and Todd were sacked.