Following groin surgery after the 2018 season, Franklin took an extended break and did not feature in Sydney’s JLT Community Series.
Parker says the 290-gamer is tracking well in his recovery.
“He’s had a pretty heavy workload the last two weeks,” Parker told media at Captains Day in Melbourne on Friday.
“If he’s right to go for round one and says he’s right to go, you’ve got to trust him.
“He’s got enough experience and knows his body and knows if he’ll be right to go.”
Franklin played 19 games in 2018 but was hampered by the injury throughout.
The Swans travel to Marvel Stadium next Saturday night for their round one clash with he Bulldogs.