The Match of the Day presenter made the promise to Outlander actor and Killie fan Steven Cree on Twitter.
The ex-England international famously wore a pair of boxer shorts when the Foxes did the unthinkable and won the English Premier League in 2016 following a similar promise.
Steve Clarke’s men currently top the Scottish Premiership after a 2-0 win over Livingston on Wednesday night edged them ahead of Rangers and Celtic at the summit.
Outlander actor Cree tweeted Lineker, and said: “Dear @GaryLineker, if Kilmarnock end the season top of the league will you present Match of The Day wearing a killie top? Or killie pants if you really want.”
Lineker replied: “I’ll do Killie socks” with Cree retorting: “I’ll knit them myself!!”
The tweet has since been liked more than 3,400 times and retweeted close to 500 times.
Kilmarnock’s last league success came in 1965.