Piastri finished FP2 in fifth, four tenths behind the leading Mercedes of Lewis Hamilton and narrowly ahead of Red Bull's Verstappen, who appeared to run with a dialled down engine as Red Hull focused on race performance.
The Australian thought the times were "much closer" than expected, but was intrigued to see how much pace Red Bull has been keeping back, only to unleash it in qualifying and the race.
"Red Bull don't look quite as quick as we thought, we'll see how many sandbags come off tomorrow," Piastri grinned when speaking to F1.com.
"It's a lot closer than I expected. Mercedes looked quick, Fernando looked quick. It's always a bit hard to judge on a Friday, but I think we're sort of around the points."
"With the teams we're around, being near the podium or near 10th is very much a possibility, so hopefully we can stay near the front of that mix."
Piastri said the team still needs to investigate some inconsistencies with the MCL38's pace, although the windy conditions at Sakhir played a part in that.
"I think we're in a decent place," he added. "Still a bit inconsistent and up and down, so it's hard to know exactly how we will fare but it looks a similar story for everyone.
"There's some runs we need to look at in more detail as to why they were how they were, both good and bad, but I think the overall feeling of the day is pretty positive.
"It always feels a bit pathetic blaming the wind on stuff but it's difficult out there when it's so windy. These cars have such a different balance and such a different amount of downforce depending on what the wind is doing.
"It was tricky out there and tomorrow is going to be more of the same."
In the second McLaren, Lando Norris finished bottom of the timesheets after abandoning his initial qualifying simulation on soft tyres.
But despite admitting he had a "messy day", he agreed with Piastri that the overall picture looked encouraging for the Woking team.
"It was a decent day, probably a little bit better than I was expecting overall," he said.
"Not my best day, just a bit messy from my part. Hopefully I got that out of the way and I can do a better job tomorrow.
"A good day for us. We tried some things, we progressed with understanding the car a bit more, but plenty of things still to try and improve on.
"It's clear that Red Bull are still towards the top and Ferrari are close, Mercedes is always a question mark, they were never going to be bad."
