The 33-year-old needs just 71 more to overhaul Cook's 12,472, and if his run spree continues he may become the new record-holder in the match starting on Monday in Multan.
"I'd like to get more than that in this game," he said of Cook's record. "I feel like I'm going to be playing for a good while past it, so it's not really a focus."
Root is a veteran of 146 Tests and already holds the record for hitting the most hundreds for England with 34 -- half of them since 2020.
He may now be eyeing the international record of 15,921 held by India's Sachin Tendulkar.
England clean swept Pakistan 3-0 when the teams last faced each other in 2022 -- Pakistan's first-ever home whitewash.
"Our last tour here was obviously excellent," said Root. "It's always nice to have that confidence and good memories going into any series."
This time the pitch is being baked by temperatures up to 39 degrees Celsius.
"We are just getting ready for the heat and how warm it's going to be over the five days," said Root. "We're just trying to prepare ourselves best for the conditions more than anything."
Pakistan vice-captain Saud Shakeel also aired concerns about the effect of high temperatures on the grass cover of the pitch. "Considering the heat, we will take everything into account," he said.
Despite the conditions, Shakeel vowed to pressure England's aggressive style of play.
"England always plays attacking cricket and the more they play like that you get more opportunities to catch them," he said. "So we will try to force more and more mistakes from them."
