Benitez led the Anfield club to Champions League glory in 2005 but guided the Reds to only seventh place in the Premier League last season. The 50-year-old has been linked with a move to Inter Milan, with the Italian giants looking for a coach following Jose Mourinho’s move to Real Madrid.
Benitez’s agent has said he will speak with the Spaniard on Thursday. BBC Sports News correspondent Dan Roan said: "Members of Liverpool’s board were locked in meetings as late as 2330 BST on Wednesday night.
"Benitez is currently on holiday but if he decides to accept their offer he could be out by the weekend." The manager’s agent Manuel Garcia Quilon said: "We don’t know anything more than what’s being said. Liverpool declined to comment on the rumours on Wednesday.
It has been reported that it would cost the club about £16m to pay off Benitez, who joined Liverpool in June 2004. But they are currently pursuing a compromise compensation package worth £3m.