30-year-old Bessone has been offered a trial at Reaseheath after being released from Millwall last season.
The former Barcalona 'C' player could be offered a contract if he impresses the management team and has had league experience at Swansea City, Leeds United, Swindon Town and Oldham Athletic as well as Espanyol 'B' and Gimnastic.
He last played league football for Millwall in their 1-0 defeat against Blackpool back in March.