The Everton midfielder joined United on January 11 and his month-long loan at Elland Road is set to end after Tuesday night's npower Championship fixture at Middlesbrough.
"I'm going to talk to Ross himself and (Everton manager) David Moyes," Leeds boss Neil 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.
"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.