The midfielder is in the final year of his current contract at the club and missed the vast majority of last season following a series of injury layoffs.
He did however return to full fitness during the turn of the year and featured heavily in Roberto Martinez's side throughout February, putting in some impressive displays and earning rave reviews.
Those performances have seemingly convinced Roberto Martinez that the player is worthy of a new deal at Goodison Park, despite his injury problems thus far, and the Blues will sit down with him before the end of the season.
However, the Republic of Ireland international will have to wait until the club have completed the bulk of their transfer business before any new deal is discussed.
The question of whether Gibson deserves a new deal however, is a hard one to answer.
His performances last season showed he still has the quality to be an important member of the side, although whether he is worthy of a starting first team place ahead of other players is debatable.
Given his injury record as well, a new contract could be deemed as some as being a bit reckless from the club. If he can maintain his fitness next season though, the Blues have a very capable squad player on their books, further strengthening them ahead of the new season.