The Foxes have set a valuation of £50 million for the talented attacker, who is unlikely to remain at the club if they are relegated to the Championship.
Leicester are in a precarious position, sitting in 18th place in the Premier League ahead of the final day of the 2022/23 season.
The looming threat of relegation further diminishes the likelihood of Barnes staying at the King Power Stadium.
Even if they avoid the drop, other top-flight teams will likely make enticing offers to prise him away.
If an offer of around £50 million materialises, Leicester will struggle to hold on to Barnes.
However, the potential transfer fee could decrease if the Foxes go down to the second tier.
West Ham are keen on acquiring the swift-footed winger. He would be a valuable addition to their squad and provide them with another dynamic option in attack.
Villa are also eyeing Barnes as they strive to bolster their options under the guidance of manager Unai Emery.
They may be a more attractive proposition for Barnes, particularly if they qualify for Europe next season.
Moving across the Midlands would result in less upheaval for the winger, which may factor into his decision this summer.
It remains unclear where Barnes will ply his trade next season, but Leicester will face a significant challenge to retain his services if a substantial offer is made.
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