The Monegasque currently sits 63 points adrift of reigning champion Verstappen after he crashed out of the lead in the French GP last time out.
Ferrari, meanwhile, trails Red Bull by 82 points in the constructors' championship.
Carlos Sainz will start second in Budapest behind first-time polesitter George Russell, and his Ferrari teammate Leclerc will line up form third in his F1-75.
This comes as a power issue in Q3 for Verstappen and subsequent strife trying to bypass the triggered sensor consigned him to 10th place.
He is due to start only one position higher than teammate Sergio Perez, who struggled for the duration of qualifying despite having a lap for violating track limits reinstated.
But Ferrari's drivers feel there's no need to intervene by holding talks over team orders or a split strategy to specifically cover off Red Bull and inflict the most damage, according to its drivers.
Asked by Motorsport.com if specials measures were required to pounce on the Red Bull woe, Leclerc said: "Honestly, at the end, we need just to do the best job possible.
"So, we focus on ourselves. I don't think there's anything needed there. We just obviously [must] not take any risk in between the cars. But that's as normal.
"So, I don't think any anything special [is required] for tomorrow."
The seven-time polesitter in 2022 added: "Max is starting 10th, so it might take him a bit more laps to come back to the front.
"But we'll just focus on ourselves and try to win the race."
Teammate Sainz reckons similarly that Ferrari's best bet to inflict maximum damage on Red Bull will be to focus solely on deposing Russell and claiming the win.
He said: "Tomorrow our target is to win the race. [We're] not focused too much where Max is because we know that if we want to cut points in the championship, the easiest way to do that is by winning.
"Independent of where Max is, we want to go for the win."
