Ronald Koeman has refused to comment on "rumours" linking Joe Hart and Lamine Kone with moves to Everton.
England No 1 Hart will leave Manchester City in the current transfer window, according to Sky sources, after Pep Guardiola picked Willy Caballero for his first two games in charge.
Everton are Sky Bet's favourites to sign Hart, and one Sky source says Goodison Park is his preferred destination, but Koeman would not comment when he was asked about the City goalkeeper at his weekly press conference.
"What I don't like is to talk about rumours," he said. "They could go on for two weeks more, with so many players linked with Everton.
"Today Joe Hart, tomorrow someone else, I prefer I don't comment on speculation linking us with players under contract at other clubs."
Koeman did say Everton were still in the market for signings and added: "We need three goalkeepers. We have Joel [Robles], we have Maarten [Stekelenburg], we have a young goalkeeper... it's all about a decision that we need to make."
Sky sources say Everton have bid £18m for Kone, but Koeman's position on the Sunderland centre-half was the same.
"He's still playing for a different team than Everton so I don't speak about him," the manager said.
Koeman was more forthcoming on the futures of Aiden McGeady and Oumar Niasse, the striker who has started just two games since arriving for £13.5m earlier this year.
He said: "We will make a fast decision about Niasse and about McGeady, maybe one or two or three more.
"It will be very difficult for them to be part of the team because we have a big squad. If [Niasse] likes to play football he needs to leave."
New arrivals Yannick Bolasie and Ashley Williams could both make their debuts at West Brom on Saturday, and Romelu Lukaku is in contention, but Seamus Coleman will not play until after the international break.
"Yannick will be part of the squad," Koeman said. "Whether he starts or is on the bench, we will decide. Yannick is fast, strong, gives the team energy. He is one of the best wingers in the league.
"Ashley is close to being part of the team. Maybe he will be in the squad for Saturday."