The Daily Record report that Kevin Blackwell has held talks with the Parkhead club and agreed an initial loan deal with a view to making the move permanent.
Agathe has not played for new Celtic boss Gordon Strachan but could resurrect his career with Leeds. Middlesbrough have also been eyeing the 30-year-old Frenchman, whose contract is up at the end of the season.
Agathe is a midfielder who likes to get forward, but can also drop back and play a deeper role if required.
He started his career in France with Montpellier but his first team chances were limited and he decided to move to Scotland with Raith Rovers and signed for the Stark's Park club on a free transfer in 1999.
The midfielder made a dream debut when he scored a hat-trick in a 4-1 win over Airdrie.
After a season with Rovers he moved to Hibernian on a three-month contract. He scored four goals in six appearances for Hibs before turning down the offer of a contract extension to join Glasgow Celtic for a reduced fee of around £50k.