The seven-time grand slam champion has been sidelined since suffering the problem at the Barcelona Open in April, missing the defence of his French Open title and Wimbledon.
Alcaraz has posted videos of himself making a tentative return to the court in the past couple of weeks, but it appears he is targeting the Masters event in Cincinnati, beginning on August 13, for his comeback.
The 23-year-old is not on the entry list for the preceding Masters event, the National Bank Open in Montreal beginning on August 2.
However, playing in Cincinnati would at least give him some match practice ahead of the US Open later in August, where he is also the defending champion.
Meanwhile, Britain's No.1 Emma Raducanu does not appear in the field for either event as she continues her recovery from a stress fracture in her lower right leg.
Raducanu withdrew on the eve of Wimbledon because of the leg issue and is facing a race against time to be fit for the US Open, which starts on August 30.
The Brit took the tennis world by storm when she won the 2021 US Open, becoming the first qualifier to win a grand slam singles title.
And the top-ranked British man, Arthur Fery, whose ranking soared to No.36 thanks to his brilliant run to the Wimbledon semi-finals, earns direct entry to a Masters event for the first time in Cincinnati.
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