Verstappen has led the standings since his second-place finish in the Turkish Grand Prix, at one stage opening up a 19-point cushion after his win in Mexico that has now been clawed back to eight going into the final two races.
Hill feels that in closing the gap, seven-time champion Hamilton again "has a spring in his step".
Speaking on the F1 Nation podcast, the 1996 champion added: "He's been getting better and better.
"He does this. He goes off on this semi-engaged period in the middle of the season, and then when he needs to finish off the championship he becomes a completely and totally focused individual."
Hamilton happy to be the hunter - Hill
Asked, though, whether he would rather have Verstappen's eight-point lead or be in Hamilton's shoes with the seemingly quicker car at present in the Mercedes, Hill added: "Well, Lewis likes to be the hunter, doesn't he?
"So he's happy where he is - hunting. But he's precious few opportunities to make up the deficit.
GPFans is a multi-platform, multi-language brand dedicated to Formula One coverage. We bring you all the ins and outs of the sport, 24/7, everything from up-to-the-minute news and features to the latest viral stories and clips.
We believe that a new generation of exciting, outspoken drivers will make F1 more popular than ever before, and we want to give our users access to as much of their heroes as possible, on and off the track. From Lewis Hamilton to Max Verstappen, Daniel Ricciardo to Sebastian Vettel, we provide in-depth analysis of every every Grand Prix in the season, from Australia to Abu Dhabi.
With Formula One under the new ownership of Liberty Media, how the sport is being covered is evolving, and GPFans will look to be at the heart of this progression into new media, as one of the fastest-growing sites covering the king of motorsports.