The Welsh captain helped his side to a 2-0 victory over Hungary in Cardiff on Tuesday that secured their place at next summer’s European Championship.
After the game, Bale and his team-mates laughed as they were pictured with a Welsh flag with the message: “Wales. Golf. Madrid. In that order.”
The images have caused a stir in the Spanish capital, where Bale has already come in for heavy criticism amid doubts over his commitment to the club.
Sources inside the Spanish club have told ESPN FC that Real Madrid believe it was “a joke in very bad taste.”
Senior figures at the Bernabeu said there is “anger, but also indifference” about Bale’s behaviour as tensions continue to build between the player and his employers.
The Merengues players are understood to have seen the funny side of the incident, but they are concerned it could further damage the forward’s relationship with the supporters.
Bale, who came close to sealing a move to China in the summer before Real pulled out of the deal at the last minute, hasn’t featured for the club since October.
He picked up an injury then and returned just in time to help his national team qualify.
Before the game, the former Tottenham star suggested that he prefers playing for Wales over Real Madrid.
"With Wales, I'm speaking my own language and feeling more comfortable," he said. "It's like playing with your mates down the park on a Sunday."
He added: "I've tried to get back as quick as I can. If there had been a Real Madrid game this week, I would've been fit. Maybe to them it doesn't look great but it's just a kind of coincidence."
Real Madrid face Real Sociedad in La Liga on Saturday.
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