If the Spaniard does start, it will be his first tournament since he got injured in the first round of the Barcelona Open in April.
Alcaraz subsequently pulled out of tournaments in Madrid and Rome and then Roland Garros, where he was the reigning two-time champion.
He also missed Wimbledon, where his rival Jannik Sinner prevailed for the second year in a row on the London grass against the German Alexander Zverev, the world No. 2, who himself had triumphed earlier on the Paris clay.
With this possible return in Cincinnati, Alcaraz could regain some rhythm before defending his US Open title at Flushing Meadows at the end of August.