Speculation about such a move erupted at the Abu Dhabi Grand Prix when it emerged that earlier this year Hamilton’s father Anthony had suggested in a conversation with Red Bull team boss Christian Horner that he touch base with the seven-time champion.
It is understood that Horner did try to contact Hamilton about an informal chat, but the message never got through as he had used an old mobile number.
In the meantime, Hamilton has since committed himself to a new two-year contract at Mercedes and his focus is on trying to help the German manufacturer get back to the front of F1.
While fans may have been intrigued about the potential for a Hamilton-Verstappen line-up, Red Bull chiefs have never appeared particularly eager about the idea.
And Marko, who has played an instrumental role in driver decisions at the Milton Keynes squad, said there are two factors that rule out the possibility of the pair ever racing together with his outfit.
Asked by Autosport about the Hamilton story, Marko said: “Christian informed me and showed me the text message he received, but I told him: ‘Hamilton and Max, that doesn't work.’
“There was too much action and how should I say, in 2021, tension. And on the other hand, we cannot afford to have the two most expensive drivers in one team.
“It's just never going to happen. So I told Christian: ‘No way.’”
While Hamilton’s future with Mercedes was not finalised until late August, he has made it clear that he never questioned his commitment to stay with the squad that has delivered six of his crowns.
Asked by Autosport if there was ever a moment during the Mercedes contract talks that he thought he might retire or move elsewhere, he said: “No, not when we were doing negotiations.
“I do have faith that we will get there. We have been here before as a team and while we have more and more new people, we still have great values, and I see great focus within everyone.
“It’s just having really good conversations with everyone back at the factory that they actually make the changes and make the right decisions, and that so easily can go the wrong way.
“I think for this year they thought the fundamentals were good and it was not the case. That’s why I was frustrated in February because they hadn’t made the changes I’d asked [for].
“But with the changes we are making, I hope we are right. But I guess we have no idea what the Red Bulls are going to do.”