Williams, 44, played two doubles matches in preparation for her comeback to singles tennis at the All England Club, but lost in the first round last week.
The 23-time Grand Slam champion then had to withdraw from the doubles with sister Venus due to a knee injury suffered in the defeat by Australian Maya Joint.
"I'll leave it to her to discuss her medical stuff and how she's feeling, but I know that for her trying to play, certainly something before the US Open will be something she would like to do," Stubbs told reporters at Wimbledon.
"She doesn't want to go and do what she did here, which was just play singles, at the US Open, but at the same time it's going to depend on physically how she's doing."
There are WTA 1000 events in Toronto and Cincinnati ahead of the US Open, which starts on August 30.
Serena, who returned after almost four years away from professional tennis, has not confirmed her next steps.
"She's got a lot of things to consider, her family, her businesses. But her goal is to keep going," insisted Stubbs, who expected her to find life easier on hard courts, the surface on which Williams has won 13 major singles titles.
"Getting on the hard court will be a lot more stable for her. And we all know how well she plays on hard court," Stubbs said.
"So it's just a matter of getting her body back into the shape she wants. And then we'll see."
Wimbledon 2026
Wimbledon is taking place from June 29th to July 12th at the All England Club in south-west London. With 128 players in the draw, it is the third of the four Grand Slams of the tennis season and the only one played on grass.
Men's singles draw and results | Women's singles draw and results | All you need to know about the tournament | Find all our Wimbledon coverage here
