Bernabeu boss Carlo Ancelotti has relegated Casillas to the substitutes bench in recent weeks, prompting the Madrid legend to weigh up a move away from the La Liga giants.
Spanish source Marca claim the 32-year-old stopper fears a lack of first-team football would put his spot in the Spanish national team in jeopardy, and is open to a potential summer switch.
Spain boss Vincente Del Bosque has quelled speculation suggesting Casillas' World Cup spot is at risk, and has offered the Real Madrid legend his public backing.
"We should associate Iker with many years representing Spanish football," he said.
"He has 149 international caps and that's no mean feat.
"We should be kind, respectful and appreciative with him and with those competing with him."
Premier League rivals Arsenal and Manchester City have both been linked with moves for the World Cup winning 'keeper, with Arsene Wenger on the lookout for a new goalkeeper having seen a move for QPR's Julio Cesar fail to come to fruition earlier in the window.
Arsenal's current no.1 Wojciech Szczesny has had a mixed start to the season and there are doubts about whether he will fulfil his potential.
Meanwhile, Manchester City are on the lookout for a new stopper to increase competition for current starter, Joe Hart.