The Japanese manufacturer said on the eve of the start of on-track running for this year's 88th edition of the French classic that Kobayashi's pole-winning 3m14.791s effort from 2017 could be within reach if track conditions are favourable.
In 2018, the pole time was 3m15.377s set by Kazuki Nakajima, while last year Kobayashi claimed the top spot with a 3m15.497s.
This weekend, the Toyota TS050 Hybrid is running 7kg heavier than it did in 2019 owing to the new Equivalence of Technology rules, with the car now 17kg heavier than it was in 2017.
However, the chances of getting a clean lap have been boosted by the new-for-2020 'hyperpole' qualifying format, which will see the top six cars in each class from Thursday's first qualifying session getting the track to themselves.
#7 Toyota Gazoo Racing Toyota TS050: Mike Conway, Kamui Kobayashi, Jose Maria Lopez
Kobayashi himself said he is keen to better his own record, knowing that the introduction of slower Le Mans Hypercars for the 2021 running of the race would mean that the existing benchmark would stay in place for some years afterwards.
"Once you get the record, you want to break the record [again]," said the Japanese driver. "It’s going to be important this year because we have hyperpole, so there’s more chance to be alone on the track.
"Once we’ve got a record this year, I guess it’s going to stay longer, because next year we have the hypercar which will be a bit slower than what we have now.
"I want to break the record, and keep it longer. The next 30 or 50 years would be nice!"