Verstappen ended Honda's podium and win droughts in 2019, the first year of its new partnership with Red Bull, and praised the manufacturer regularly throughout the season.
He also pointed to the Honda badge on his race suit when he stepped onto the podium at the Austrian Grand Prix, the scene of Honda's first F1 win in 13 years.
Verstappen's three victories in 2019 have already moved him level with the likes of Keke Rosberg and Gerhard Berger on Honda's list of winners.
That list is topped by three-time world champion Senna, who won 32 grands prix and three world titles between 1987 and 1992 using Honda engines.
Honda's F1 managing director Masashi Yamamoto told Motorsport.com: "As Honda, we see him as a very important factor with Honda's project.
"He's young, but his driving is really impressive. It looks like seeing a young Senna, with his relationship with Honda.
"Max maybe pays respect to Honda. He feels Honda is familiar. And then probably the badge he showed on the podium in Austria proved that he was very happy as well.
"This gives us an emotion that we want to provide a good engine for him. Of course, all the four drivers are very important for us."
Verstappen told Motorsport.com last year that Honda's working practices were aligned with his and he also enjoyed seeing how emotional the manufacturer got when it achieved success.
Yamamoto said the 22-year-old had developed a close affinity to the brand.
"The passion we showed towards winning made the relationship stronger with him," said Yamamoto. "He also has been to the F1 R&D centre and our mass production site.
"There's many, many people [working at those facilities] and he has actually seen it. He went through a tunnel of people getting high fives, like one kilometre long!
"That kind of thing maybe gave him a stronger impression about Honda, and a stronger commitment to Honda."