Liverpool want a decision from Luis Suarez by the end of the month.
The Mirror says Suarez has three weeks to sort out his future.
After that, the controversial striker will be expected to knuckle down and commit himself to the Liverpool cause.
The Uruguay international has been given until Monday July 22 to take a holiday in South America following Confederations Cup duty that only ended last Sunday, before reporting back to the club he has repeatedly said he wants to leave.
No decision has yet been made on precisely where the forward will be told to join his team-mates, but it is almost certain he will be ordered to take part in the Reds' tour of the Far East and Australia.