The Mali international – who is rumoured to have rejected a switch to Liverpool in January – is set to be a free agent when the next transfer window opens after only signing a six-month contract with Valencia over the winter.
Although he is rumoured to be keen to stay, the Spanish side may opt against keeping the 34-year-old, which would leave him as an option for Everton.
Keita made over 100 appearances for Barcelona, where he won the Champions League in 2009 and 2011 as well as numerous other honours, before leaving to join Chinese side Dalian Aerbin in 2012.
His spell in the Far East was a short one, and he returned to Europe with Valencia just a few months ago after being released from his contract.
Toffees chief Roberto Martinez is said to be planning for a campaign of European and domestic action, and sees the veteran as a player that will be able to contribute to his side’s efforts next term.
The Spaniard is already facing the prospect of losing loan star Gareth Barry, whose experience and know-how have been vital in the Merseysiders’ impressive campaign.