Then the Reds made a £1m bid for West Ham winger Yossi Benayoun, which the Hammers described as an "insult".
Now a Reds source has told daily financial newspaper CityAM that Benitez has real concerns about the future ambitions of the club.
"If Gillett and Hicks cannot give Rafa a budget in which a sensible assault on the title, then Rafa will not hang around for long," he said.