MLB Pipeline has released their list of top draft prospects for next year: https://www.mlb.com/prospects/2023/draft/
Following the lottery results, this is the 2023 draft order. The Reds selections are bolded:
1-01 Pittsburgh Pirates
1-02 Washington Nationals
1-03 Detroit Tigers
1-04 Texas Rangers
1-05 Minnesota Twins
1-06 Oakland Athletics
1-07 Cincinnati Reds
1-08 Kansas City Royals
1-09 Colorado Rockies
1-10 Miami Marlins
1-11 Los Angeles Angels
1-12 Arizona Diamondbacks
1-13 Chicago Cubs
1-14 Boston Red Sox
1-15 Chicago White Sox
1-16 San Francisco Giants
1-17 Baltimore Orioles
1-18 Milwaukee Brewers
1-19 Tampa Bay Rays
1-20 Toronto Blue Jays
1-21 St. Louis Cardinals
1-22 Seattle Mariners
1-23 Cleveland Guardians
1-24 Atlanta Braves
1-25 San Diego Padres
1-26 New York Yankees
1-27 Philadelphia Phillies
1-28 Houston Astros
Compensation Picks
1-29 Seattle Mariners
Competitive Balance picks may be traded and are not subject to forfeiture.
1-30 Seattle Mariners
1-31 Tampa Bay Rays
1-32 New York Mets
1-33 Milwaukee Brewers
1-34 Minnesota Twins
1-35 Miami Marlins
1-36 Los Angeles Dodgers
1-37 Detroit Tigers
1-38 Cincinnati Reds
1-39 Oakland Athletics
Second Round
2-40 Washington Nationals
2-41 Oakland Athletics
2-42 Pittsburgh Pirates
2-43 Cincinnati Reds
2-44 Kansas City Royals
2-45 Detroit Tigers
2-46 Colorado Rockies
2-47 Miami Marlins
2-48 Arizona Diamondbacks
2-49 Chicago Cubs
2-50 Minnesota Twins
2-51 Boston Red Sox
2-52 Chicago White Sox
2-53 San Francisco Giants
2-54 Baltimore Orioles
2-55 Milwaukee Brewers
2-56 Tampa Bay Rays
2-57 Toronto Blue Jays
2-58 New York Mets
2-59 Seattle Mariners
2-60 Cleveland Guardians
2-61 Atlanta Braves
2-62 Los Angeles Dodgers
2-63 New York Yankees
2-64 Houston Astros
Competitive Balance Round B
2-65 Cleveland Guardians
2-66 Baltimore Orioles
2-67 Arizona Diamondbacks
2-68 Colorado Rockies
2-69 Kansas City Royals
2-70 Pittsburgh Pirates
Compensation picks
2-71 Giants
2-72 Braves
2-73 Chicago Cubs
Third Round
3-74 Washington Nationals
3-75 Oakland Athletics
3-76 Pittsburgh Pirates
3-77 Cincinnati Reds