The soon to be 33-year-old full-back is out-of-contract at the end of the season, but he has barely featured under Roberto Martinez this term with Seamus Coleman in imperious form and the emergence of youngster John Stones.
Hibbert has not started a league game since December 2012, but Martinez insists that the veteran offers a huge amount to the club off-the-pitch.
"At the moment it's been a frustrating season for Tony because of his injury problems which have stopped him competing for his place. John Stones and Seamus have taken advantage of being fully fit and have played games.
"That doesn't change Tony's position here though, he has the experience and understanding of the club which is massive," he told the Liverpool Echo.
"The role he has is not like other players who can only help the team by playing at the weekend.
"Tony's role is bigger than that - he comes in every morning and the standard he sets is important. He helps us develop and he will always have a role at Everton for me.
"Tony came on against Stevenage and has been unfortunate not to play more minutes since then.
"He came on against Aston Villa and showed everyone he is ready and it's a matter of just being patient now."