The 33-year old made over 200 appearances for the Trotters between 1990 and 1996 before infamously moving north of the border to join Scottish giants Glasgow Celtic in a big money move.
Stubbs is beleived to be unhappy at only being offered a one-year deal to stay at Goodison Park and could be forced to look elsewhere for the two year deal which he is craving.
Blackburn Rovers are also thought to be monitoring developments with the former Wanderers skipper who has been in excellent form for the Merseysiders this term.