This fixture is Bristol City's first friendly of the summer, while the Scottish giants have already played two games at Dragon Park in Newport.
Celtic begin their important Champions League qualification campaign next week against Midtjylland and their preparation for that game has gone well so far.
Their first pre-season friendly this year came against League One outfit Sheffield Wednesday, who took an early lead through Josh Windass, but Postecoglou's side eventually ran out 3-1 winners in that game.
Pre-season friendlies tend to be an opportunity for managers to rotate their squad and find their best 11 for the new season ahead, and so far Postecoglou's selection between the posts has cast goalkeeper Scott Bain's future into doubt.
Bain ended the 2020-21 season as the Hoops' number one, but in both matches this summer Vasilis Barkas has started in goal, suggesting that the Greek shot stopper will be Celtic's goalkeeper moving forward.
The Robins did not manage a single win in their last 10 games which brought the 2020-21 season to a defeating end, and their lowest Championship finish since their return to the second tier in 2015.
However, the club are backing Pearson to guide the side higher up the table next season after he has a full pre-season with the squad, starting on Wednesday against Celtic.
Bristol made their first summer signing earlier this month with Andy King joining on a free transfer, having spent his childhood growing up as a Robins fan.
A second signing of this transfer window came shortly afterwards as centre-back Rob Atkinson arrived for an undisclosed fee from Oxford United, penning a three-year deal at Ashton Gate.
Bristol City's Championship campaign begins at home against newly-promoted Blackpool on August 7, and they will be hoping to replicate their opening day from last season when they beat Coventry City 2-1.
Celtic centre-back Christopher Jullien has been sidelined since December with a knee injury and is expected to be absent on Wednesday again, but he could make his return to action this month.
Striker Odsonne Edouard has been heavily linked with a move away from Celtic Park this summer, amid interest from Leicester City and Arsenal, but he has come into the side for the second half of both friendly fixtures so far.
Andreas Weimann missed a large portion of the Championship season last year, being absent from the side since October, but he has made a return to fitness and will be in contention to start against Celtic.
Bristol City possible starting lineup:
Bentley; Mariappa, Atkinson, Baker, Simpson; King, Bakinson; Palmer, Pearson, Weimann; Martin
Celtic possible starting lineup:
Barkas; Taylor, Bitton, Urhoghide, Ajer; McGregor, Turnbull; Ajeti, Dembele, Henderson; Edouard
We say: Bristol City 1-2 Celtic
Celtic should be the sharper of the two sides having played two matches already this summer, and Bristol City may need some time to get up to match fitness.
Postecoglou's side have been in fine form in front of goal this summer and will be a tough test for the Championship outfit's defenders, especially if Pearson opts to hand young Atkinson his debut.