Sauber, running Sutil's car without a drinks bottle so far in 2014, has managed to cut 'substantial' weight from its Ferrari-powered C33 for the Spanish grand prix this weekend.
Reports indicate it could be as much as 15 kilos lighter than before.
"I don't want to say numbers, but it is important that we are close to the (minimum) limit now," Sutil is quoted by Speed Week.
"You can never build a 'too light' racing car."
Still, it is suggested that Sutil's disadvantage will continue in Spain, as only Gutierrez is actually slightly beneath the FIA's mandatory limit, allowing him to position ballast around the car to improve handling.
Sutil has been critical of the sport's reluctance to further increase the weight limit, as it has driven naturally heavier drivers to ramp up their dieting regimes.
He told reporters on Thursday that he has experimented with fasting.
"I was testing it a little bit here and there," said Sutil. "Two days, no food, only drink.
"It was not easy but interesting what the reaction is. I could feel there was a limit where I didn't have the power any more, the strength in my mind. It's just important to know your body quite well.
"I tried it but I'm still alive so don't worry too much," he told reporters.