Everton manager Roberto Martinez insists he has had no fresh approaches for Leighton Baines or Marouane Fellaini.
Manchester United had a £12 million bid for left-back Baines rejected at the end of June, while Arsenal have been linked with midfielder Fellaini for much of the summer, although have not submitted an offer.
Martinez, appointed on June 5 after Everton's former manager David Moyes agreed to take charge at Manchester United, is keen to keep both players at Goodison Park. Asked at a press conference if he had received recent bids for either player, Martinez said: "Not at all."
He was then asked if he was surprised that United had not followed up their initial bid, and said: "No. The last concern that I have is what the other clubs do.
"If we get clubs talking about our players, I take it as a compliment because the players have been doing very well. We're in a great position financially, we're very strong and we want to start the season with the best possible squad."
Martinez indicated last month that he planned talks with Baines to extend a contract that runs until 2015. The 28-year-old enjoyed an impressive season, scoring his first England goal against Moldova in September and earning a place in the PFA's Team of the Year.
Fellaini, who has been linked with Manchester United as well as Arsenal, has a stipulation in his contract that allows him to speak to clubs in the Champions League who submit a bid of £22 million or more.
But it is understood that the clause has a time limit to protect Everton from losing him too close to the transfer deadline of September 2.
Everton chairman Bill Kenwright confirmed that there was a clause in the 25-year-old's contract last month, but warned Moyes off trying to sign Everton players.
Kenwright said at the time: "I've not said to David: ‘David, come on'. I've said exactly the opposite. I've said to David Moyes: 'We all know the situation at Everton. We all know there's a player who's got an escape clause, but the others are not for sale'."