Meanwhile, the hosts - who currently sit fifth in the table - would move to within four points of the summit if they were to come away with all three points.
Match preview
Cincinnati extended their unbeaten MLS run to four matches when they played out a 2-2 draw away against New England Revolution on Monday.
Brazilian forward Brenner scored for the third successive game and helped rescue a point for the Orange and Blue by netting a 73rd-minute equaliser. The 22-year-old has now found the net five times in the last three MLS matches, the same total he notched up in his previous 31 appearances.
That result has seen Cincinnati move onto 25 points from 18 matches, setting a new club record for points accumulated in a single regular MLS season - surpassing the 24 collected in their inaugural 2019 campaign.
Pat Noonan's side will now prepare for a challenging fixture against the league leaders, although their recent record against New York Red Bulls will provide them with a boost heading into Sunday's contest.
Cincinnati have claimed seven points from the last 12 available against the Red Bulls and have kept three clean sheets in the process.
Victory for the Orange and Blue this weekend cannot see them climb up the table from fifth position, as they are currently four points behind New York City FC in fourth and CF Montreal in third.
After suffering a 2-0 away defeat to Los Angeles FC at the end of June, New York Red Bulls have since claimed back-to-back victories this month against Atlanta United and Sporting Kansas City.
A dramatic 2-1 win over Atlanta - a game which they were losing heading into the final seven minutes - was followed by a slender 1-0 success away at Kansas City with 10 men.
Aaron Long scored the only goal of the game with a close-range header in the 53rd minute, before Sean Nealis was shown a straight red card following a VAR review after he was deemed to have deliberately handled the ball as the last man.
Nevertheless, the Red Bulls managed to hold on to claim all three points for the ninth time this season, and that result has seen them climb to the Eastern Conference summit following Philadelphia Union's goalless draw with Columbus Crew.
Gerhard Struber's side have now won six MLS away games this season, which can only be matched by Austin; only three times in their 28-year history have they won seven or more MLS away games in a single campaign, winning seven on the road in 2002 and eight away from home in 2000 and 2018.
With challenging fixtures against rivals New York City FC and Austin on the horizon, the Red Bulls will be keen to build on their momentum and claim maximum points on Sunday.
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Team News
Cincinnati defender Ronald Matarrita faces a lengthy spell on the sidelines after undergoing ankle surgery, while Dominique Badji, Junior Moreno and Calvin Harris are all ruled out with leg injuries.
Former Manchester United youngster Tyler Blackett could return to the starting lineup at the expense of Ian Murphy, joining Nick Hagglund and Geoff Cameron in the back three.
Attacking trio Luciano Acosta, Brandon Vazquez and Brenner, who have scored a combined 19 goals so far this term, are all expected to keep their places, with the former operating in a number 10 role behind the latter two strikers.
As for New York Red Bulls, Sean Nealis will serve a one-match suspension following his dismissal against Kansas City, with Tom Edwards likely to replace him at the heart of the defence if he recovers in time from a minor ankle problem.
Andres Reyes is also doubtful with a foot issue, while Lucas Monzon and Wikelman Carmona are both ruled out with respective hamstring and foot injuries.
Teenagers Caden Clark and Daniel Edelman recently helped the USA Under-20s win the CONCACAF Championship title, and although the pair are set to return to the Red Bulls, they are unlikely to feature on Sunday.
Top scorer Lewis Morgan, who has eight MLS strikes to his name so far this season, is expected to start again on the left flank, while striker Patryk Klimala will be hoping to replace Tom Barlow in the first XI.
FC Cincinnati possible starting lineup:
Celentano; Hagglund, Cameron, Blackett; Powell, Kubo, Moreno, Nelson; Acosta; Vazquez, Brenner
New York Red Bulls possible starting lineup:
Coronel; Edwards, D. Nealis, Long, Tolkin; Amaya, Casseres; Luquinhas, Fernandez, Morgan; Klimala
We say: FC Cincinnati 0-1 New York Red Bulls
Only one of the seven MLS encounters between Cincinnati and New York Red Bulls has seen more than two goals scored, so a closely-fought contest could be on the cards in Ohio.