The centre-forward, who sustained cruciate knee ligament damage during a season-long loan spell at Derby County last term, is already working out under the guidance of the Owls' conditioning experts.
Manager Jos Luhukay, whose side begin their Championship campaign at Wigan Athletic on Saturday, believes the 27-year-old is heading for a mid-August reunion with his teammates.
"He's now two or three weeks back training," Luhukay said. "He's making progress, but he needs a couple of weeks before he can come back to the team training."
Winnall isn't expected to be available for selection until the end of September.
He scored six goals in 18 Rams appearances - which included six starts - before his season was ended by the injury he suffered against Brentford on February 3.
"He had surgery," Luhukay said. "Normally, this kind of injury takes six months. He is in this time period. He needs more time to come back 100 per cent."
Winnall joined Wednesday from Barnsley in a £500,000 deal in January 2017 and scored four goals in 16 league games (11 starts) before then-manager Carlos Carvalhal sanctioned his temporary switch to Derby three games into last season.