Adam Pearson confirmed that the duo have been offered "very attractive" two year contracts.
Whitmore started his Tigers career very well, becoming an instant hero on the terraces with his sublime skill. However, tragedy affected his form after a car crash left him slightly injured and Jamaican team-mate Steve Malcolm dead a year ago. "Tappa" was placed on the transfer list in the close-season, but was given a second chance after impressing in pre-season.
Goodison didn't enjoy such a good start, failing to claim a place in the starting eleven while being played out of position. However, Brian Little's appointment gave "Pepe" a chance at centre back and the 29-year-old firmly established himself with the Tigers, picking up the Player of the Year award in May.
Pearson said that the proposals are currently with the players' agents.