The Reds responded to interest in one of Rafa Benitez's favourite players by declaring Benayoun not for sale on Wednesday.
"We spoke to Benayoun on Wednesday," said Dynamo sporting director Konstantin Sarsania. "He said that his meeting with the Liverpool directors had been rescheduled for Thursday.
"The position of the football club, reflected on their official website, is known to us, but the footballer himself insists on the sale."
Dynamo say they have already agreed terms with the 29-year-old, who saw a similar move to Spartak Moscow blocked last year.
But a Liverpool spokesman said on Wednesday: "The player is not for sale, it's as simple as that."
However, Sarsania insisted it was not the end of the matter.
"The negotiation process continues," he said. "Liverpool have not ruled out the transfer. We are still in touch with Benayoun's agent and we still believe the transfer can happen."