Barkley will enter the final six months of his Everton contract in January and would be eligible to sign a pre-contract agreement with another club but there is speculation that he could also be tempted away in a permanent transfer as well.
Chelsea almost signed the 24-year-old over the summer but the move collapsed at the last minute and the London club could return next month with an offer to both the Blues and the player to sign him.
Barkley's difficult relationship with Ronald Koeman was cited as a possible reason why he didn't sign a new contract over the summer and there is hope at Goodison Park that he could yet commit his future to Everton now that the Dutchman has gone.
Allardyce admits he doesn't have much say in the matter but he holds out hope Barkley could end up staying.
“It's a difficult one,” the manager said in The Guardian. “I haven't had the opportunity yet to find out the truth, or the whole scenario, to ask: ‘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' [with an offer] and the club says: ‘Look, if he's not going to sign for us this has to be the case,' then I accept that.
“If Ross stays until the end of the season and I feel he is giving 100% to the team, like he has done since he was a kid, then he is an available asset for us until he leaves on a free transfer. I would hate that to happen but it might do.”
Allardyce was quizzed on Barkley again during his press conference ahead of Monday's game against Swansea and he repeated his stance that he hasn't spoken to the player about his future.
He agreed, however, that it would probably make sense for Everton to listen to cash offers for him in January if he is set on leaving rather than letting him go for just a development fee in the summer.
“There's been no contact from Chelsea that I'm aware of. If that materialises then that discussion would happen between all the various people in the club from the top down to me to make the best decision for the football club.
“If Ross isn't interested in staying at Everton — and I don't know whether he is or if he isn't at the moment — then it would be sensible to consider any offers there are in January.
“But at this moment we're speculating because there is no offer to consider. At the moment, Ross is recovering from an injury. I'm more interested in Ross Barkley being fit and available because he is an Everton player at the moment.”