Watford have announced the signing of Italy international Marco Motta, subject to international clearance.
Mark Noble has signed a new deal with West Ham which will keep him at the club until the summer of 2020.
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 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."
Hay turned down a move to Oldham - now bossed by former Killie team-mate Lee Johnson - for family reasons earlier this summer but the Scotland B cap insists he is still good enough to play in the Scottish Premier League.
But the player insists he is frustrated by the lack of offers.
"I still have haven't got anything lined up," he said. "It's been pretty quiet on the football side of things.
"A few managers have taken my number but there has been no offers so far.
"I'm not really surprised that it's been like this, though. There are lots of boys out of contract right now and there are plenty of players available for managers to choose from.
"I'm a bit older and maybe coaches aren't looking for someone as experienced as I am. It's just one of those things.
"I'd like to get in somewhere and get started with training. I've still got a year or two left in me fitness wise.
"If it doesn't happen I'll just have to live with it, but I know in myself that I've still got a year or two left in me at a decent level."
Hay is currently working towards his Elite Youth coaching badge and added: "I'm interested in the coaching side of things and I've done all my badges. I just want to stay in the game. Football is all I have known."