Oviedo has been a regular starter for FCK after joining from Deportivo Saprissa in his homeland.
The 22-year-old, who can operate at left-back and on the left side of midfield, is en route to Merseyside to undergo a medical and discuss personal terms.
Everton's pre-match press conference this morning ahead of Saturday's Barclays Premier League away clash with West Brom was conducted by Toffees assistant boss Steve Round, who explained that manager David Moyes was in London working on finalising the Oviedo deal.
Asked about Oviedo, Round said: "I have seen him on a regular basis - I have been abroad and watched him, as have all the scouts and the manager.
"But as yet he is not our player. We have work permits to get. That is why the manager is not doing the press today - he is in London trying to tie that up and finalise it.
"Until it's all done we can't really comment too much, but I think later in the day it will all become clearer and when he puts pen to paper we can talk about the player.
"He can play left back, left midfield, left wing - all the way down the left hand-side. That will give us good cover in our squad."
Source: PA
Source: PA