The midfielder joined the Whites on January 11 and his month-long loan at Elland Road is set to expire following Tuesday's Championship fixture at Middlesbrough.
Leeds boss Neil Warnock is staying fairly tight-lipped over Barkley's immediate future and plans to speak to his counterpart at Everton, David Moyes, over the highly-rated youngster.
"I'm going to talk to Ross himself and (Everton manager) David Moyes," Warnock told his club's official website. "He wasn't in the starting line-up on Saturday so I'm going to have a chat with them. I'm sure we'll decide over the next 24 hours.
"He has done well, he is a good young lad and he is going to be a top player one day. We'll have to wait and see, not just on Ross but on our targets as well that we are trying to bring in. We are still trying to get a wide player."
He added: "That's why I had the conversation with David when I knew that he wouldn't be starting against Wolves and we agreed to talk on Tuesday."
Barkley has made four appearances during his loan spell with the Whites but has yet to score for the West Yorkshire play-off hopefuls.