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World number five Dominic Thiem said on Saturday making next month's US Open will be "very, very tight" after he pulled out of Wimbledon with a wrist injury.
The New York tournament, where Austrian Thiem won his only Grand Slam in 2020, starts on August 30.
"Up until the US Open it will be very, very tight," he told Sky Sports Austria.
"I can't guarantee or promise myself anything."
"Even before my title, New York was my favourite tournament. Having a comeback there would be a dream, but it will be difficult.
"I will work hard towards that."
Thiem has endured a tough season and even before his injury had said he would skip the Tokyo Olympics to concentrate on defending his US Open title.
He was knocked out of the French Open in the first round despite being a two-time runner-up in Paris and then had to retire from his opening match in a grass court event in Mallorca.
In the interview Thiem gave more details of the injury in his right wrist that he suffered last week.
"I have a small tear in the tendon sheath and in the capsule around it," he said.
Thiem said he was having to spend "99 percent of the day" with his hand in a splint and would have to continue doing so for another three weeks.
He added that his current medical advice was that the splint may be necessary for even longer "until I am fit for competition again," giving him a tight timetable to make the US Open.