The winger is currently lighting up the World Cup and the former Reds defender claims Brendan Rodgers failed with a move for the Bayern star in 2013
The Bayern Munich winger has scored three goals for his country at the 2014 World Cup, with Louis van Gaal's side set to face Costa Rica in their quarter-final on Saturday.
And Carragher says Rodgers made a move to sign the star last year, at a time when the 30-year-old was struggling for game time at Bayern – with the defender claiming such a move would have been perfect for both parties.
"Brendan Rodgers tried to sign him for Liverpool before the 2013 Champions League final,” he told the Daily Mail.
"He wasn't a regular for Bayern then but he scored the winner at Wembley against Borussia Dortmund and has since gone from strength to strength.
"Liverpool have not had a world class wide man since John Barnes."
Former Chelsea and Real Madrid star Robben signed a new contract with Bayern earlier this year, which would keep him at the Allianz Arena until 2017.