The 32-year-old lost his place to Iker Casillas at the end of last season and is poised to drop to third choice with the imminent arrival of Keylor Navas.
The 32-year-old established himself as coach Carlo Ancelotti's preferred choice for Liga games last season, only to then lose his place to Iker Casillas during the closing stages of the campaign.
Madrid has had a deal in place to sign Costa Rica international Keylor Navas for several weeks - a move that will finally be ratified on Monday after president Florentino Perez asked Levante to delay confirmation until the squad has returned to Spain from its preseason base in the United States.
After weeks of uncertainty over the goalkeeping situation with three top-level keepers set to be on the books, Perez led discussions over the issue after joining up with the group this week.
Following talks, club sources now say Lopez is likely to be the man who slips down to third choice in the race to start. Consequently, he is prepared to leave the Santiago Bernabeu and will speak to Madrid in the days ahead after considering his options.
Ancelotti has decided that Spain international Casillas will begin the 2014-15 campaign as first choice - despite his error in last season's Champions League final against Atletico Madrid and a calamitous showing at the World Cup.
The Italian coach has also indicated that he does not want to rotate his goalkeepers as much as he did during the 2013-14 campaign, meaning Lopez's chances of nailing down a regular berth in the Blancos lineup are even slimmer.
A departure for Lopez would leave new arrival Navas clear to put pressure on Casillas, who is now set to stay at the club having been linked with a move away earlier in the summer.
Madrid is expecting a number of sides to express an interest in Lopez after he racked up 62 appearances in a successful 18-month spell at the club.
The former Villarreal and Sevilla shot stopper still has three years left on his Madrid contract.