The veteran full-back was released by chairman Michael Johnston when his contract expired at the end of last season.
The 35-year-old had been tipped to pair up with Jimmy Nicholl in a coaching roll to replace Kenny Shiels when the Northern Irishman was sacked following controversy over his out-spoken media comments.
But Killie chief Johnston appointed his namesake from Queen of the South instead and Hay was allowed to leave, despite having racked up 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 told Press Association Sport: "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."
- Sports & Recreation
- Jimmy Nicholl
- Kenny Shiels