The Mercedes boss found himself on the receiving end of scathing remarks from Mintzlaff over the Miami Grand Prix weekend, with the energy drinks company's managing director not happy about Mercedes trying to lure Verstappen away from his current squad.
Mintzlaff told Bild Am Sonntag: “I understand the pressure that Toto Wolff and perhaps other teams have after years of being behind. But I think Toto Wolff should concentrate on his challenges. He has enough of those.
“And it also has something to do with respect. If I keep talking about the personnel of other teams, that's not right.”
Wolff is totally unmoved by what was said, though, and suggested that what Mintzlaff was talking about was irrelevant to him.
“I don't know what this guy is commenting on,” said Wolff. “It has no relevance for me.”
There were reports – which Wolff has denied – of Mercedes lining up a meeting with Verstappen and his representatives this week to discuss a potential 2025 deal.
However, Wolff has made clear that he continues to keep a watching brief over developments, although it is too early to be definitive about his squad’s second driver plans for 2025.
“There's always plenty of meetings,” he said. “I can't really say [anything definite] about the second driver. I think we've talked about the possibilities, and I want to be fair to these guys and not make it look like we are playing chess with humans because we are not doing that.
“We want to take our time, see where Max's thinking goes and, at the same time, monitor the other drivers.
“Carlos [Sainz] was very strong today again and that's why we are a little bit on an observation mode at the moment.”
While Mercedes waits to see what Verstappen decides in the end, its other obvious option is junior driver Andrea Kimi Antonelli.
The Italian youngster was at the centre of speculation over the Miami weekend about a potential step up to Williams soon, with it understood that the squad has asked the FIA for an F1 superlicence exemption for him because he is under 18.
Wolff said that Mercedes has no interest in him racing in F1 now as it wants him to focus on doing his best in F2.
“So many stories were created, and it doesn't do him any favours because he needs to concentrate on his F2 campaign,” added Wolff.
“He's doing lots of testing for us in order to bring him up to speed and I think this decision of the second driver is weeks if not months away. We didn't make any approach to the FIA about getting an earlier release.”