TheÂ boss is adamant the academy product willÂ become a 'very good player' '“Â but feels he must develop his game when out of possession.Â
May is striving to establish himself as a starterÂ in the Blues' engine room after signing a new two-year contract this summer.Â
The 20-year-old impressed in Pompey's friendly win at Bognor last month, netting a hat-trick in the 5-1 victory.
However, he was an unused substitute in the Blues' 1-1 draw against FC UtrechtÂ on Saturday.
Anton Walkes and Tom Naylor occupiedÂ the middle of the park against the Dutch side. They are likely to retain their berths for the League One curtain-raiser against Luton in two days' time.Â
Regardless, Jackett believes May hasÂ '˜all of the tools' to feature for PompeyÂ week-in, week-out.
But improving off the ball will be key to the Eastleigh-born talent achieving that.
The manager said: '˜He has all of the tools, Adam. You look at the size of him, he can run and has a good shot on him.
'He has all of the tools but just needs to put it all together. He'll earn that spot by showing he can put it all together '“Â which I think he is capable of.
'He would describe himself as an attacking midfielder. He still has to learn not to switch off and react in defensive situations.
'It's not just defensive situations but off the ball as well. Off the ball, he has to switch on when the ball is behind him.
'He can't be out of the game '“Â you can't be out of the game mentally as a holding midfielder.
'For Adam, he has to pick up that side of things. He has a lot of ability and I have a lot of time for him '“Â he's definitely going to be a very good player.
'He has a range of passing but defensively and off the ball is where he has to work at league level. They are things that will get him on the ball more and get him involved in the game more '“Â he's got a lot of talent.'
Naylor has immediately stamped his authority on Pompey's midfield since arriving earlier this summer.Â
Jackett reckons May can learn from the ex-Burton man.
The boss added: 'If you watch Naylor, he's always moving, talking and adjusting.
'˜Tom has a lot of league games and a different age bracket to Adam. He doesÂ well in terms of his defending, covering and talking which makes him available to getÂ on the ball more.'