Bale confirmed his intention to move on after nine years in the Spanish capital when his contract expires at the end of June.
After leading Wales to their first World Cup spot since 1958, Bale hinted he is close to a decision over his club future, with a string of offers on the table for the 32-year-old.
According to reports from BBC Sport, EFL Championship side Cardiff City are the front runners to secure a free transfer move for Bale.
Previous links to former club Tottenham, or the MLS, appear to have ended in recent weeks, with his focus on the World Cup in Qatar in November.
Bale is only likely to sign a short term deal in the Welsh capital, and he could retire after leading Wales at the tournament, or at the end of 2022/23.