The News of the World says he held showdown talks with Benitez after being axed from last Monday's Premier League fixture with Aston Villa.
His current contract runs out in 18 months, and the left back almost moved to Villa Park in a £7m deal last summer.
By his own admission, Riise's form has dipped alarmingly this season, but it was the first time in seven years at Anfield he'd been dropped from the 16-man squad for a league game.
That prompted an angry response, but Benitez will feel no sympathy for the 27-year-old who was ordered to buckle down and work on his game.
Villa and Newcastle are monitoring Riise's position and are likely to make a £6m move for defender in the summer.
Kevin Keegan would like to tempt Riise to St James' Park even sooner and is weighing up an offer before the end of the week.