The Pompey boss believes the teenager can handle the physical challenge he will face in the third tier next season.
Jackett is currently weighing up whether to turn to the academy graduate in the middle of the park in the coming months.
May will be out to impress the 55-year-old against Hawks today (3pm), as he revealed Wolves made enquiries about signing him when he was in charge at Molineux.
It looks like it could be a big campaign ahead for the talented passer after spending time out on loan at Sutton United in the National League last season.
Jackett has been impressed with the early impressions May has made after Pompey returned for pre-season training.
With May, Ben Close and Danny Rose making up the holding midfield contingent, the Blues appear to be a body light in that area.
But Jackett believes the 19-year-old could be ready to be turned to after three senior starts and four substitute appearances to date.
Despite there being physical development to be made for May, Jackett believes he could handle being thrown into the heat of a League One midfield battle.
And the club’s new boss would have no reservations about doing that, if May sends the right messages in the coming weeks.
Jackett said: ‘I’m well aware of Adam. Very much so.
‘Wolves did make enquiries about him at one stage to go into the development group.
‘I personally did not see Adam play but Wolves as a club did.
‘Looking at him in pre-season you can see he has a good passing range.
‘He can run, too. I’m looking forward to working with him.
‘I understand he hasn’t got much in the way of experience.
‘But he has the basics to be a good player and I’m looking forward to working with him.
‘He’s going to be an interesting player for us this season.
‘He’s a decent stamp of a lad. He will get stronger, I do agree with that, and he will fill out.
‘But he’s not small now by any stretch. He’s big enough.
‘I’d say that he’s big enough now.’
Meanwhile, Pompey remain hopeful they have won the battle to land keeper Christian Walton.
Walton is the priority target to be their No1 next season, with the 21-year-old set to leave Brighton on loan.
Wigan are the Blues’ keenest rivals for Walton’s signature and discussions with the player are ongoing.
Jackett remains interested in Dagenham & Redbridge striker Oliver Hawkins.
Pompey have made their interest known but are not prepared to meet the Londoners’ valuation of the 25-year-old.
Nathan Thompson and Tareiq Holmes-Dennis are the two arrivals to date.