Elsewhere, A-League champions Adelaide United will travel to face Queensland's Redlands United while Green Gully host Central Coast Mariners and Melbourne City take the trip west to tackle Floreat Athena.
Meanwhile, the three all A-League clashes see Brisbane Roar play Perth Glory, Newcastle Jets take on the 2015 FFA Cup champions Melbourne Victory and Wellington Phoenix at home against Western Sydney Wanderers.
This year’s list of entrants includes 11 clubs making their first appearance in this stage of the FFA Cup, including: Bonnyrigg White Eagles (NSW), Canberra Olympic (ACT), Cockburn City (WA), Devonport Strikers (TAS), Floreat Athena (WA), Green Gully (VIC), Lambton Jaffas (Northern NSW), Marconi Stallions (NSW), Redlands United (QLD), Rovers Darwin FC (NT) and Surfers Paradise Apollo (QLD).
The 16 fixtures will be held over three weeks, with four matches per night set to commence in the last week of July.
Sydney FC coach Graham Arnold said he was pleased with the draw, with the Sky Blues set to start pre-season training on Monday.
"We’ve got something to aim for now in the first round, playing a very motivated Wollongong Wolves team, and we’re looking forward immensely to the challenge," Arnold said.
Reigning A-League premiers and champions, Adelaide United will travel to Queensland for their clash with Redlands United and coach Guillermo Amor said they will be ready for a tough match.
"At this stage, we do not know a lot about how Redlands United play their football, but we have time to do our research and we will have to be ready for a tough match away from home," Amor said.
"They have done very well to qualify for this tournament and they will have some momentum when they play against us."
Full FFA Cup round of 32 draw is:
Brisbane Roar v Perth Glory
Newcastle Jets v Melbourne Victory
Wellington Phoenix v Western Sydney Wanderers
Wollongong Wolves v Sydney FC
Redlands United v Adelaide United
Green Gully v Central Coast Mariners
Floreat Athena v Melbourne City
Melbourne Knights v Cockburn City
FNQ Heat v Edgeworth Eagles
Rovers Darwin v Brisbane Strikers
MetroStars v Bentleigh Greens
Canberra Olympic v Surfers Paradise Apollo
Devonport Strikers v Lambton Jaffas
Bonnyrigg White Eagles v Manly United
Hume City v Marconi Stallions
Blacktown City v Sydney United 58