The Dutchman has won two of the last three races and is 62 points behind leader Lewis Hamilton with 10 races to go.
“I don’t think we are favourites but we will try to do a good job,” Verstappen said.
“With Mercedes having had such a dominant start to the season, it is really hard to catch them. We are going to try but I am not thinking about the title.”
Verstappen won a chaotic race in Germany last weekend and also in Austria two races before that. He missed out on a podium at Silverstone in between Austria and Germany only when he was rammed by Ferrari’s Sebastian Vettel, but still finished fifth.
“For them, being more than 60 points in the lead is massive,” Verstappen said. “They had a bad weekend but it can also happen to us.
“It is still a big gap to close.”
The 21-year-old predicted Mercedes would be especially determined to bounce back at the Hungaroring after a difficult race last Sunday in Germany, where Hamilton was ninth and team-mate Valtteri Bottas crashed.
“If you look over the whole season so far, Mercedes has been the most dominant and especially after last weekend they will come here to try to bounce back from that,” Verstappen said.
“They will try everything to do a good job here.”
For many, Verstappen has arguably been the driver of the season so far, and he said he was benefiting from the experience of now being in his fifth season.
“Knowing when to peak and when not to, when to take a risk and when not to, all these kinds of things help,” he said.
Hamilton said “time would tell” whether Verstappen and Red Bull would have the consistent pace on every type of track to challenge.
“He has done a great job and they have clearly done a great job in quite a few races now,” Hamilton said.
“In the last one we didn’t do such a great job. It made their job look even better. They will be quick here and places like Singapore where they’ll be strong.
“They are, in general, catching up. It is great to see them progressing. We want the competition and we’ll ready for the fight whenever it comes.”
Hamilton said after the Germany race that it had been one of his worst weekends – he crashed after leading the first 29 laps of the race and damaged his front wing, then was given a five-second penalty for incorrectly entering the pits.
Late in the race, he had a spin trying to make up lost ground and was only promoted into the points when the two Alfa Romeos were disqualified for a technical infringement.
“I don’t have any negative feelings or carry any weight from that weekend,” Hamilton said. “It was just a bad day and a difficult weekend. These things happen but a multitude of things contributed to it.
“The team has had some really open and honest discussions, and come out of it positive. There have been adjustments made by all parties.”
Hamilton was also unwell in Germany, battling an infection, but he said after resting over the past three days, he is feeling better.
“I am hoping to be 100% by the weekend,” he said.
Hamilton’s team-mate Valtteri Bottas missed a golden opportunity to reduce his championship deficit to the Briton in Germany when he crashed late in the race.
And when Hamilton was promoted into the points, it meant the Finn actually lost ground, and is now 41 points behind.
On top of that, Bottas knows team boss Toto Wolff is waiting until the mid-season break, which falls after this weekend, before he makes a decision on whether to retain Bottas for 2020.
But Bottas said he was not concerned about his future.
“For sure it was not ideal in terms of that, but it happens,” Bottas said. “A mistake happened at the wrong time. I was trying hard, which is what the team wants to see. But I don’t think one mistake is going to change anything.
“That is my mindset. I should not think about it and I need to perform at my best and focus on that. I know I can do well. Then it is up to the team. But no stress. Full gas.
“I am still in the championship fight. Maybe some people don’t believe it, but I still know it’s possible.”