Michael Bryan and Ryan Bird will be given the stage at Westleigh Park to prove their worth to Pompey.
Guy Whittingham is seeking to give the two triallists starts in the Blues’ first friendly of the season against the Hawks next Tuesday.
The duo are the only unsigned players currently training with Pompey’s new-look squad.
Both played non-league football last season, with striker Bird featuring for Burnham in Southern League division one central and ex-Watford winger Bryan ending the campaign with Corby in Blue Square Bet North.
Whittingham will cast his eye over the pairing this week before allowing them the chance to shine against the Hawks in the traditional pre-season encounter.
The Pompey boss said: ‘They both will be here for the remainder of this week and for the Havant game as well.
‘We will see how they go. If they impress we will probably want more than just that game – if they don’t they will probably get less!
‘I think it is fair to say they have got a chance to become full-time professional players here.
‘We will give them the opportunity to impress and I hope they will do.
‘With Ryan, it will be interesting to see how he goes because non-league training is very difficult and some players I have known from non-league trying to make it haven’t been able to because of the fitness side of things.
‘Sometimes the body just isn’t ready to go into full-time training.
‘Although we want him to come in and work hard and enjoy himself, we have also got to be careful and aware he is not used to the full-time training.
‘So we are just monitoring and making sure we give him every opportunity to impress.
‘Michael is one of those who had his opportunity. It didn’t come his way but he can be encouraged we are giving him the opportunity here.
‘In training, you’ve got sessions where you are using not just fitness but are looking at their football brain as well and technically whether they are good enough to play at this level.
‘We are not looking at doing much tactically football-wise probably until early next week.
‘At the moment it is all about getting people back in the way of kicking a football because when you haven’t done it for so long, you have to coordinate a bit better, your muscles have to get eased gently into it.
‘Things will slowly increase next week and there will be a more tactical side of training – and we will keep looking at the pair of them.’
Pompey have been known for their large intake of triallists in pre-season during recent times.
Last year, nine of them never earned deals, having appeared in friendlies at the likes of Gibraltar, Aldershot and Salisbury.
Others such as Simon Eastwood, Jon Harley, Luke Rodgers, Liam Walker and Josh Thompson won short contracts.
Whittingham believes other triallists will arrive next week, most likely after the Hawks friendly – although not on the scale employed previously by the Blues.
He added: ‘There possibly might be other triallists next week.
‘What we didn’t want to do is flood the place with triallists because we did that in January and it was horrible.
‘We were trying to find players to get us to the end of the season and it wasn’t fair on players here.
‘You are trying to build a team spirit so you can’t have lots of different faces in and out all the time.’