Alcaraz takes on the qualifier and 70th ranked Max Purcell of Australia today also in the quarterfinals.
Djokovic could possibly meet the 16th seeded Alexander Zverev of Germany in Saturday's semifinals before facing Alcaraz in Sunday's final.
Djokovic won the Australian Open in January before also taking the title at Roland Garros in June.
However Djokovic's bid for a historic calendar Grand Slam ended this year in a final round loss at Wimbledon to Alcaraz.
The US Open, the year's final grand slam tournament is set to be played in New York City August 28 through September 10th.
Should Djokovic fail to regain the top ranking in Cincinnati, he will have a greater chance in New York where Alcaraz as the defending champion will be defending 2,000 points to none for Djokovic.