The Spain international has fallen behind Diego Lopez as first choice at the Santiago Bernabeu and both the Reds and the Gunners are monitoring Casillas's situation in Madrid, according to The Metro.
Despite denials from Los Blancos coach Jose Mourinho, several reports have suggested that the pair have fallen out this season and that Casillas will be allowed to leave for the right price this summer.
Arsenal manager Arsene Wenger recently questioned the mentality of current Gunners keeper Wojciech Szczesny ahead of their Champions League exit at Bayern Munich.
Meanwhile, reports have persisted all season that Liverpool boss Brendan Rodgers is prepared to sell his own No. 1 Pepe Reina at the end of the campaign, with Barcelona linked with the Spaniard.
Casillas was part of the Spain squad that won the 2010 World Cup and Euro 2012.