Bale, who joined Madrid in 2013, has scored 67 goals in 146 appearances and signed a contract extension in October to keep him at the club until 2022 but his future in Spain has been cast in doubt following a frustrating injury-riddled campaign.
"We are winning trophies and I am happy. I have signed a long-term contract at Madrid," Bale is quoted as saying by the BBC after Madrid beat Juventus 4-1 in the final in Cardiff.
"My family is happy and I am happy, so yes we will continue what we are doing."
Madrid's third Champions League triumph in four years marked Bale's seventh trophy at the club but the 27-year-old remains hungry for more success.
