The German – who trounced Alejandro Davidovich Fokina for a Roland-Garros semi-final berth on Tuesday – found the chatter, if anything, relieved him of some of the pressure.
Zverev: The end goal hasn't changed
Sixth seed cruises past Davidovich Fokina to reach maiden Roland-Garros semi-final
Far from content to hide in their shadows, however, the 24-year-old has laid down his challenge to whichever of the pair he meets in the last four.
"Obviously the Grand Slams are the tournaments that we want to win the most. Before, maybe the last few years, I was putting too much pressure on myself," Zverev said, following his 6-4, 6-1, 6-1 victory. "Also obviously in the media I was seen, before Medvedev and Tsitsipas arrived, I was seen as this guy that was going to all of a sudden take over the tennis world...
"I was not very patient with myself, which I feel like now maybe I learned how to deal with the situation a little bit better, I'm maybe a little bit calmer at the tournaments. But the end goal hasn't changed."
In a scrappy first set, which included seven breaks of serve, the sixth seed snuck it to seal the advantage over the 22-year-old, who had never advanced this far on such a stage.
Davidovich Fokina had hoped to become just the second Spanish man other than Rafael Nadal to reach a Roland-Garros semi-final since 2005, after David Ferrer.
But the emotional and physical toll of his path to the second week had started to show.
Zverev – who had claimed both prior encounters between the two – only struck his first ace at 1-all in the second set as he nudged his first-serve percentage closer to 50 per cent, but from there it was smooth sailing.
He cantered home at the 96-minute mark against an ailing opponent, who conceded he was suffering a back complaint.
“After the first set I think my baseline game improved a lot. I started to dominate the points much more,” Zverev said on court. “In the beginning I didn't think I played that well. I think I can play better, hopefully.
“Obviously he's someone who's improved a lot over the past year and a half. He's climbing up the rankings very quickly. It's his first quarter-final of a Grand Slam and I'm pretty sure it's not his last.”
After he improved his five-set record at the majors to 4-0 with a nail-biting four-hour, 35-minute upset of in-form Norwegian Casper Ruud in the third round, Davidovich Fokina likened his mentality to that of a marathon runner.
Zverev could liken his to a high-jumper, having finally raised the bar on his Grand Slam record in the past year.
Rapid to rise the ranks on tour, but slow to hit his straps at the majors, the German had reached just one fourth round in 12 main draw attempts before he finally notched his maiden Grand Slam quarter-final. That came in Paris four years ago.
His first major semi-final followed at last year’s Australian Open, before he went one better, only to fall from two sets up to Dominic Thiem in the US Open final last September.
For the third time he has closed to within two victories.
"I'm in the semi-finals of a Grand Slam and I played solid so far," Zverev said. "I know that the matches [from] the semi-finals on are not going to get easier. I think the opponents there are extremely difficult to beat, so I got to play the same or raise my level even higher to have a chance.
"But I'm comfortable. I'm happy. We'll see how it is on Friday. But for now, it's great to be here."
The 46th-ranked Davidovich Fokina was the highest-ranked player Zverev had faced en route to the last four.
While the draw gods had been kind to him to this point, he knows he needs to lift a gear, whichever of the heirs apparent he meets next.