The Yorkshire Evening Postclaim Ayling is close to agreeing a three-year deal with the Elland Road club.
The 24-year-old is said to have completed a medical and is set to become Leeds' eighth signing of the summer.
Garry Monk reportedly moved for Ayling following Sunday’s 3-0 defeat to Queens Park Rangers.
Leeds' first choice right-back Gaetano Berardi was taken off during the game with a hamstring injury leaving the Whites short of defensive options.
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Leeds have agreed a three-year deal for Luke Ayling
Ayling is said to have been on Celtic's radar and the Daily Record claimed Brendan Rodgers was keen to sign the right-back.
The report said Rodgers was hopeful of a deal after Bristol signed former Celtic defender Adam Matthews on a season-long loan.
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Ayling started his career at Arsenal but made a name for himself at Yeovil in 2010.
He joined Bristol in 2014 and has since made 80 appearances for the club and won the League One title in 2015.