Barkley has refused to sign a new deal at Everton, and Allardyce feels that decision is purely a financial one.
And the former England boss has warned Barkley that he has left himself in a position where he could be putting his career at threat.
"It’s all about this money thing. 'Everton, my boyhood club aren’t offering enough money'. His agent is probably saying that he can get more money elsewhere," Allardyce said.
"A move to Tottenham I believe broke down due to the money. He’s left in limbo and he’s putting his career in severe danger here.
"If Chelsea don’t come in, or they don’t offer the money he’s looking for, then what do they do then?
"He needs to get back to playing football. Whatever the contract is, surely it’s going to be enough to stay at Everton are move on."
Barkley has not featured at all for Everton this season, due to injury.
The attacking midfielder seemed to have burned his bridges with former boss Ronald Koeman, but David Unsworth has been more open to Barkley staying.
Allardyce’s words are particularly interesting, as he could take over at Goodison Park.
Allardyce is among the leading contenders to take over from Koeman at Everton.