Federer remains the all-time leader but has not been able to add to his tally since winning Wimbledon in 2018.
World No 1 Novak Djokovic (16) has closed in significantly after winning four of the last five Grand Slams and he is the favourite ahead of the US Open.
In June, Nadal won his 18th major title when he won a 12th French Open and will also be favourite to make it 13 in 2020.
It all means Federer, who turns 38 next month, is facing the increasing prospect of losing his most prized record.
Speaking in an interview with Spanish publication El Confidential, Bautista Agut was asked who he thought would end up with the most Grand Slam titles.
And the Spaniard gave an interesting response.
“For now, Federer is the one who is leading,” Bautista Agut said.
“Although because of his age, he has the least options left to continue extending his record.
“In my opinion, it will depend a little on Rafa, who by age is closer to Djokovic and has also managed to adapt to all types of surfaces.
“What I do know is that, whatever happens, the three of them will be remembered for everything they have achieved.”
The dominance of Djokovic, Nadal and Federer has been a source of complaint from some critics.
But Bautista Agut feels the sport owes the trio a debt of gratitude.
He added: “They have raised the level of our tennis to another dimension. They force us to be better.
“Tennis lives a moment of splendour like never before in history thanks to their rivalries.
“That this sport is healthy and beautiful is largely their fault.”