According to The Sun, the 30-year-old defensive midfielder is wanted by Toffees boss David Moyes to bolster his squad which will head into the New Year competing for honours both at home and in Europe.
Albelda, along with fellow stars Miguel Angel Angulo and Santiago Canizares, has been left out of Ronald Koeman's squads for Valencia's final two games of 2007 as the Dutch coach attempts to make a significant mark at the Mestalla following a dreadful start in the hotseat.
It is believed he fancies a move to England but Everton could face competition from Pompey, who the Daily Mirror report as also being interested.
Koeman said: "They'll not be in the squad again before the winter break and then we'll make decisions about the future.
"I want to change things at the club and give opportunities to other programmes."