Kenny Jackett wants to see James Meredith in match action before deciding whether to step up his interest.
The left-back has been trialling with the Blues for almost three weeks as he seeks to earn a Fratton Park deal.
Meredith is a free agent after his Millwall contract was cancelled by mutual consent in the summer.
Jackett has been assessing the Australian since Lee Brown sustained an Achilles injury against Coventry in the middle of last month.
Brandon Haunstrup has since stepped up to replace Brown at left-back, producing impressive form in the process.
Yet Meredith, who Jackett believes can also operate on the left-hand side of midfield, remains in his thoughts.
And following the scrapping of the reserves’ Premier League Cup match against Doncaster, the next available outing to blood the 31-year-old is at the Hawks in the Hampshire Senior Cup (September 18).
Jackett said: ‘There are some games coming up – and that’s the plan with James.
‘His situation is that, after maybe 2-3 weeks of training to get up to speed, the back end will then see him play a game or two.
‘At that point, we will be able to reassess him and work James towards full fitness to get the best out of him.
‘We do understand that if something comes up in the meantime then he will speak to the another club, I do see that.
‘But, similarly, we have to do what is right for this club, which is having a look at him in training and possibly a game or two.’
Richard Brindley is another free agent who has been training with Pompey, although last week joined Notts County.
And, in the case of Meredith, Jackett believes the opportunity to survey a player over a lengthy period of time can help with judgement.
Pompey’s boss added: ‘It’s very difficult to make a decision on a player in one day.’
‘Sometimes you have two or three days and maybe need to make a decision.
‘At other times you have to set out a plan and tell him what you’ve got to offer – then it’s up to him.’