Payne, 27, switched from motocross to speedway and joined the Potters last season in place of the injured Emerson Jones.
Payne, from Leigh in Lancashire, burst onto the scene and was consistently scoring above the 4.90 average he set in the Midland Development League.
He broke two ribs in June in a crash at Buxton and after coming back from injury his impressive form continued. He was top scorer twice toward the end of the season.
Tattum said: “Lee was a breath of fresh air.
“He was like a beacon in what was for us a very disappointing season but I have discussed matters with him and he is extremely keen to return and I expect to finalise the situation within the next few days.”
Team manager Malcolm Vasey added: “We plan a very fresh looking team and we see Lee as having a massive future in speedway.
“His development has been meteoric and I expect him to continue in that vein.”
Payne told StaffsLive: “I hope to better myself even more and keep moving forward, all I can ask of Stoke is to do the same as this year, they gave me a chance and they looked after me well.”
The Potters management will attend a National League AGM along with representatives from nine other National League teams at Rugby.
Tattum said: “Certain matters will be clarified at that meeting and it will enable us to determine our precise approach to 2014.
“I am determined the club will move forward from last season and be challenging for honours.
“Lee is the first brick in the wall and we intend that the wall will lead to a fortress for 2014.”