Hennessey has not featured at first-team level for 14 months after twice injuring cruciate knee ligaments.
He will return to full training with the rest of the squad next week but new boss Jackett has vowed to nurse him back into competitive action.
"In terms of Wayne we are going to have to monitor what he does and take it every day," Jackett told the club's official website.
"We will have to be very careful with him but basically he is confident and he is good to go.
"We will monitor his situation and treat him with kid gloves to make sure he gets through the pre-season period."
Razak Boukari, who has had surgery on his troublesome calf, is set to be the only player sidelined when his team-mates return for fitness testing on Monday.
"I think Razak is the only one who isn't likely to start pre-season," Jackett added. "Apart from Razak everybody is there or thereabouts."