Bowen missed the FA Cup loss to Bristol City earlier this week with an ankle problem sustained in the meeting with the Championship side at the London Stadium.
“He’s doing better,” said the Scotsman on Friday.
“Whether he’ll be fit and available I wouldn’t give that information out but he’s certainly doing better than we thought.”
West Ham will also be without Lucas Paqueta for the trip to Bramall Lane on Sunday, with Moyes admitting he has “no idea” when the Brazilian will return.
“I have no idea," he said.
"No idea on that. I don’t look at social media so I couldn’t tell you what pictures he’s posted, what he’s been doing in the gym. Couldn’t tell you if it’s work that makes him get himself get ready faster or if he’s needing his tendon injury to heal a bit longer. Sorry, I couldn’t give you any more on that.”
Pablo Fornals and Edson Alvarez, meanwhile, face late fitness tests as the Hammers look to get back on track following their dismal cup exit at Ashton Gate.
“They’re okay, we’ll see how they are those two and Jarrod we’ll need to make late calls tomorrow and see if they’re able to travel or not,” added Moyes.