The Ghana global made 24 Premier League appearances in 2015-16 as the Foxes won their first title.
Crystal Palace hope to strengthen across their back four this month and have entered talks with Leicester City over defender Jeffrey Schlupp, but West Bromwich Albion remain the player's preferred destination after lengthy talks in the summer.
The full-back or winger will be available to play in Palace's Premier League match at West Ham on Saturday.
The 24-year-old will move if the Eagles meet the Foxes' asking price, which Press Association Sport understands to be close to £12million.
"I am delighted we have been able to secure Jeffrey's services", Palace manager Sam Allardyce, said as reported by the club's official website.
"He will bring strength and experience to the defence and will be a major asset for the club".
"We wish him every success and look forward to welcoming him back to King Power Stadium as both an opposition player and friend of the club".
He said: "He's of course not happy. If the right money arrives he can go", he said.
Zeki Fryers, who had been deemed unworthy of Palace's 25-man Premier League squad in previous seasons, was registered and Martin Kelly has started in the role for much of the campaign.
He scored a hat-trick on his Leicester debut - a 4-1 League Cup win over Rotherham in 2011 - and made 150 appearances for the Foxes, netting 15 goals.