Griezmann himself encouraged further talk of a shock move to Santiago Bernabeu, however, when he admitted that he could not rule out the prospect of joining the club in future.
And Ramos says the Madrid squad would have no problem embracing the arrival of the 26-year-old, who scored the equaliser for Atletico in the 1-1 derby draw on Saturday.
"We'll see, these types of signings make a lot of headlines and he's a great player who's been proving himself for a few years," Ramos told the media.
"Madrid always opens its doors to great players."
The position of Madrid boss Zinedine Zidane has also come under scrutiny, with the former France star suggesting that his future is out of his hands despite his side challenging for a league and Champions League double.
Ramos was unwilling to speculate but made it clear that a failure to win silverware could be decisive.
"I'm not the right person to talk about the coach's future, at the end of the season, titles will decide everything," he said.
Madrid dominated the derby but failed to add to Pepe's header early in the second half before Griezmann snatched a point, but they were given a boost in the title race when Barcelona suffered a 2-0 defeat to Malaga.
Ramos was disappointed with Madrid's result but is now looking forward to a significant two weeks of the season, with league matches against Sporting Gijon and Barca plus a Champions League quarter-final tie with Bayern Munich coming up.
"It will be a final, just like every game between now and the end of the season if we want to win LaLiga," he said of the Clasico on April 23. "We have to keep scoring three points in each game.
"Atletico's best players were their defenders and goalkeeper, that tells you everything.
"You have to move on, in football there's no time to mourn and the game against Bayern is another final as we try to reach the last four."