The Toffees have already strengthened this summer with the arrivals of Richarlison and Lucas Digne.
Brazil attacker Bernard has completed a medical at Goodison Park.
The defender has been heavily linked with a move to Everton but faced late competition from Manchester United.
Everton will be keen to give Gomes a chance to remind his form, with the talented midfielder left out of the Portugal squad for the World Cup this summer. My understanding, I've spoken to somebody in Spain this morning, is that one is very, very close to being done.
Lord Pickles Backs Calls For Boris To Apologise Over Burka Remarks
A source close to Johnson said, "We must not fall into the trap of shutting down the debate on hard issues". The former foreign secretary used his column to comment on Denmark's introduction of a burka ban.
It follows a window which saw them offer under the odds for Harry Maguire and Jerome Boateng, about whose fitness they had reservations, while they refused to meet the demands of Yerry Mina's agent and didn't even register an offer for Spurs' Alderweireld.
The Everton manager also let Ashley Williams leave the side on loan to join Stoke City and Ramiro Funes Mori was allowed to join Villarreal.
Usually in cases such as this clubs can approach the Premier League and request more time to complete the deal, if they can provide all the necessary paperwork and prove that the completing the deal is just a matter of dotting i's and crossing t's. There's been plenty of names, clubs who have been after him.
However, Chelsea did not want to sell the player to a direct rival and Everton appear to have won the race to sign the player.