Liverpool have increased their offer to sign Real Madrid midfielder Asier Illarramendi. The Premier League club are understood to have already had a €15 million offer for the Basque midfielder knocked back, according to Marca, but now the Reds have returned with an increased bid. According to Marca, Madrid are now considering a €22 million offer for a player they spent €35 million on in the summer of 2013 but who has not been a success. Illarramendi was all set for the Bernabeu exit door this summer after failing to win the trust of Carlo Ancelotti but the arrival of Rafa Benitez at least gives him hope of proving his doubters wrong. Still, those high up are not convinced by the player and already accepted an offer from Athletic Bilbao in the winter transfer window only for the player to reject the move. If Madrid try to usher him out of the door again he could accept - but only if the club is right. Both Liverpool and Arsenal have shown interest in him.