Majority shareholder Farhad Moshiri said Everton had accepted a bid and Barkley had agreed terms.
But the 23-year-old tweeted on Saturday that he had not had a medical "with any club at any point".
"I decided it would be best to make a decision and assess all my options in January when fully fit," he said.
Barkley has a hamstring injury that is likely to keep him out for three months.
Listen: Which is the best club for Barkley?
Everton had initially rejected a £25m offer from Chelsea for the player on Wednesday before reports that a deal had been agreed late on Thursday.
"It is a big surprise but that is football," Moshiri told Sky Sports.
Barkley has less than a year left on his contract and has turned down a new deal at the club he grew up supporting and joined as an 11-year-old.
The academy graduate has played 150 times for Everton in the Premier League, scoring 21 times since making his debut in 2011.
In July, manager Ronald Koeman said the club "100%" expected Barkley to leave Goodison Park.