The trio finished on the podium together for the second time this season at the Canadian Grand Prix, having also shared the rostrum in Australia.
Hamilton, Verstappen and Alonso have won a combined total of 11 drivers’ titles and are F1’s only active world champions following Sebastian Vettel’s retirement at the end of 2022.
Seven-time world champion Hamilton described the Montreal podium as “iconic”.
"It's just a privilege to be up here fighting these two, who have done incredible in their careers," Hamilton said.
"This is quite an iconic top three - I don't know if there's been a top three like this ever before, I don't believe there has.
"I'm really hoping at some stage we have a more level playing field in our cars and then we'll have much more exciting races in the future.
"I'm happy to be back in the mix, and I'm just hoping at some stage we can be a bit more level so we can get back to some of the good races we had back in 2021.
"To have all three of us in a super-tight battle would be sick.”
Alonso said he thoroughly enjoyed his “very intense” but “very fair” battle with Hamilton for second place in Canada.
"It's good, it's great. I really enjoy these battles. This podium happened in Australia, I think last time, and now here,” the Spaniard said.
"There is a lot of respect, a lot of talent, when you fight against Max, Lewis, you know that you cannot make a mistake because they will take advantage of that and they will not make a mistake.
"So if you want to beat them, you need to be tenth after tenth faster to close that gap, it's not anything that will benefit.
"It's a very intense battle, very fair, very respectful. Even the overtaking possibility that we had on the DRS for me when I passed Lewis, you know that you can trust what he's doing - he will defend hard but within the limits.
“[It was the] same at the start - I guess when you start on the front two rows with these guys, there is a sense of awareness and respect that is not sometimes in other parts.”
Fellow two-time world champion Verstappen, who drew level with Ayrton Senna’s tally of victories with his 41st win in Canada to strengthen his grip on the 2023 world title, added: "I remember back in the day I was watching these two already in Formula 1 racing each other.
"So, of course, I'm very happy now that I'm in F1 as well, racing them is probably one of the best things out there.
"When we can share a podium together, we've done it a few times, I think it's great. I think they want to swap positions, of course, I'm happy in the middle at the moment."