Barkley has not featured for Everton this season as he recovers from a torn hamstring.
The 24-year-old's future has been subject to speculation for some time, particularly since the summer transfer window in which he rejected a deal with Chelsea on deadline day.
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He had been heavily linked with move to Tottenham Hotspur throughout the summer, with Mauricio Pochettino thought to be a huge admirer of the England worldwide, however it looks as though his future lies at Premier League Champions Chelsea, just days after Antonio Conte moaned about not getting the olayers he asked for.
Tottenham have been monitoring Barkley's situation but Sky Sports suggest the North Londoners have made a decision to end their interest with Mauricio Pochettino now looking at alternative targets.
"I would expect there would be [an offer] sometime in this window if there's going to be interest from one of the big boys", the Everton boss told a news conference ahead of Friday's match away to local rivals Liverpool in the third round of the FA Cup.
They would also argue that with Barkley out of the side this season, his absence has not hampered their performances - particularly since Allardyce took over from Koeman.