Kenny has barely featured for the Toffees ever since he returned from his loan at Schalke 04 last season, with the 23-year-old making just a single Premier League start, along with three other appearances from off the bench.
When Seamus Coleman has been unavailable, Carlo Ancelotti has preferred playing Mason Holgate out of position rather than playing Kenny.
As a result, he could be set to leave the club, but unfortunately for Kenny, a switch to Turf Moor is looking more and more unlikely due to Everton's asking price.
Due to Everton asking £10 million for Kenny, the Clarets have reportedly backed away, saying that the figure would use up too much of their budget.
Burnley's options at right-back are quite limited, with Matthew Lowton their first-choice, but they only have 35-year-old Phil Bardsley as their other option in the position, and they need new players in that position, especially with Bardsley's contract running out in the summer.
Selling Kenny for £10 million could prove to be a good deal for Everton, with the Englishman not really in Ancelotti's plans, but they have to stand firm and not budge from their asking price to get the right value for him.