Centre-back Seaborne is a free agent after leaving St Mary's earlier this summer.
Seaborne found himself down the pecking order with Saints last season and enjoyed spells on loan at Charlton and Bournemouth.
A number of clubs have expressed an interest, but it appears Yeovil are ready to offer the 26-year-old a two-year deal at Huish Park.
Seaborne featured for Yeovil in Tuesday's friendly defeat to Torquay and did enough to impress Glovers boss Gary Johnson.
Johnson is short of options at the back and he sees Seaborne as a key addition to his squad ahead of the new season in the Championship.