With new manager Jan Molby looking to the future, Pearson sees no point in keeping them at the club any longer.
He said: "We've made an offer which would allow them to leave now. We're waiting for a reply."
Their City careers began at Macclesfield in the FA Cup back in October 1999. Since then, Whitmore has made 93 appearances in the black and amber, while Goodison has notched up 84.
Despite excelling in previous years, this season has been a massive disappointment for the pair. Goodison has missed large parts of this season through injury, while Whitmore has struggled with form and fitness.
They rejected new contracts a few months ago, and Pearson told them then that any club who made an approach could have them on free transfers. So far there doesn't appear to have been any interest. It is thought that they will seek moves back to the Caribbean, or the MLS in America.