The 35-year-old full-back was released by Killie chairman Michael Johnston when his contract expired at the end of last season.
He had been tipped to pair up with Jimmy Nicholl in a coaching role to replace Kenny Shiels when the Northern Irishman was sacked.
But Killie chief Johnston appointed his namesake from Queen of the South instead and Hay was allowed to leave after 14 years' service with the club.
Now Hay is searching for a new side after admitting he has given up hope of returning to the Ayrshire side.
He said: "There are no hard feelings or grudges with Killie. With Kenny parting ways and Jimmy Nicholl leaving too, it was always going to be very difficult after that.
"I'm still doing stuff coaching some of the younger lads at pro-youth level.
"But going back isn't an option. I haven't heard from the new management at the club and I don't expect to. I'm looking forward now."