The England international is out of contract at the end of the season and little progress appears to have been made on him staying at Goodison Park, leading to speculation he will be sold next month.
Chelsea nearly snapped the 23-year-old up in the summer for £35million, only for Barkley to perform a U-turn, while Tottenham also made several attempts to bring him to north London.
Both clubs are thought to have retained an interest in Barkley and could reignite their pursuits in the new year, with Allardyce fully aware Everton cannot afford to let him walk away for nothing.
"It's a difficult one," said Allardyce. "I haven't had the opportunity yet to find out the true, or the whole, scenario and say, 'Where does it lie?' and then make a decision one way or the other.
"I'm not in control of that in too many ways. If someone comes in during January and says 'here you go', and the club say 'look, if he's not going to sign for us, this has to be the case', then I accept that."