The 23-year-old’s wonder-strike against Sunderland on Sunday was not enough for Spurs as Arsenal pipped their north London rivals to the final Champions League spot.
Bale scored 21 Premier League goals this season, scooping the PFA player of the year award for his performances, and Ramos backed Madrid’s pursuit of the Wales international.
“Gareth Bale is a Real Madrid-quality signing,” Ramos told the Sun.
“He has had an exceptional season. He can punish any team in the world and has the footballing qualities we look for in Madrid.
“I am sure Madrid will not be the only team that want to sign him, but he is the right mould for us.”
On Wednesday, Bale indicated that despite being disappointed with Tottenham’s failure to finish in the top four, he was ready to stay at White Hart Lane.
“We fought hard this season, the team and the manager have been great,” Bale added. “We have got the record points for the club in the Premier League,” Bale told the club’s website.
“That would normally be enough to qualify for the Champions League, but it’s not meant to be again.
“It’s disappointing, but we will pick ourselves up again.
“We will just have to regroup this season and give it another go.”
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news