Clark's Aston Villa contract expired at the end of last season, which he spent on loan to Port Vale.
And the League Two side were keen to sign the full-back on a permanent basis.
But the Vale boss, John Askey, believes Leicester will be Clark's next club - and isn't hopeful over another loan deal.
"I have been told that he has signed for Leicester," Askey told the Stoke Sentinel.
"I think if he goes to Leicester then I don't think they will loan him out until January anyway. You get to a stage where you just move on and hopefully we can get somebody in better."
Clark spent more than half of his 20 years on Aston Villa's books, but only played once for the Villans' first team.
The Welshman can play equally well at right or left full-back, where his Leicester rivals would comprise Ricardo Pereria, James Justin, Ben Chilwell, Christian Fuchs and Callum Elder.
Aston Villa have strengthened in both positions this summer, bringing in Frederic Guilbert and Matt Targett.
Would the former Villa man be a good addition for Leicester?
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