Spanish newspaper Sport claims Real Madrid do not want to lose their goalkeeper - and would demand a minimum of €20m if Casillas tried to force a move.
The Spanish number one has been in and out of the team this season - much like last term - with Diego Lopez the first-choice keeper in La Liga.
Casillas is yet to make a league appearance under Carlo Ancelotti and has been linked with Arsenal among others.
He has friends including Mesut Ozil and Santi Cazorla at the Emirates Stadium, and could be tempted by regular first-team football in the Premier League.
The report claims Madrid are concerned Casillas could decide to leave the club, and have reportedly begun drawing up a list of potential replacements.
The Spaniard faces a potentially historic summer as he leads Spain's defence of their World Cup title.
They can extend their tournament winning streak to four with victory in Brazil, following 2008 and 2012 triumphs in the European Championships and the win over Holland in South Africa four years ago.
Casillas would be an obvious upgrade over current Arsenal first-choice Wojciech Szczesny, but the Polish international is a solid keeper and the Gunners should not be desperate to change things up.
For one thing, a striker looks like a much more pressing priority.