The South African's current deal expires at the end of the season but United have offered him a one-year extension.
The deal has been agreed in principle after talks with the player and his agent and will extend Radebe's stay at Elland Road to a 10th season.
Elland Road director Peter Lorimer today confirmed in the YEP: "We've agreed a deal with Lucas. We're delighted he'll be here next year because he has been a great servant to the football club. He has had his injury problems, but a lot of that is down to the fact that he has battled so hard for this club at times when he probably shouldn't have played. That sums up the sort of man that Lucas is and we're pleased he is staying on."
The YEP also reports that the legendary centre-back has agreed in a reduction in terms because he is keen to end his career with The Whites.
Lorimer added: "He's been unbelievable for this club. Loyalty isn't always the same nowadays because of the masses of money in the game but Lucas is a loyal guy. He's never wanted to leave Leeds and I think he sets a great example to younger players. He's good to have around because he's a popular bloke and, at a time when the club may have to look at bringing younger players through, his experience will be important."
Radebe will also be able to enjoy a testimonial to mark his 10 years of service. The new board had promised they would grant Radebe a testimonial and Lorimer says it is right and proper for the former captain, stating: "Everyone wanted Lucas to have his testimonial."