Pompey expect up to three more triallists to land at Eastleigh before the week draws to a close.
But Michael Appleton is unsure whether long-time target Izale McLeod will be among them.
The 27-year-old is currently a free agent after turning down the offer of a new deal at Barnet.
The Blues have subsequently held talks this summer with the powerful striker, who last season netted 22 goals for the Bees as they avoided relegation from League Two on the final day.
Yet Football League restrictions have contrived to stop McLeod signing on at Fratton Park, with Walsall and Cheltenham among a host of other clubs interested in snapping him up.
Now Appleton is waiting to see if the former Charlton man – and any more of his targets – arrive at the training ground in the coming days.
He added: ‘There may be two or three more triallists who come in this week.
‘We have obviously spoken to players and agents but what you tend to find is you can’t expect them to be here.
‘There is a probability they might be but players get cold feet, they worry about whether going somewhere on trial will have a negative effect on them.
‘Some people see it as a positive, that “look at me, I am prepared to go out on trial and work for a contract” situation.
‘Others believe it looks bad if somebody sees them trialling and they will think “it will cost me a move to club X,Y or Z”.
‘Obviously, Izale is out of contract and when we are in a position to do something, of course I would love to get his services.
‘I am sure a dozen would love to but for us it is difficult. There are loads of players out there I want to sign and probably could sign. Yet until someone gives me the green light it can’t happen.
‘There are already players here who are out-of-contract and we thought we would have a look, see where they are fitness-wise and assess it day-by-day.
‘Look at Mustapha Dumbuya. He is one at the minute who hasn’t got a football club and is quiet happy to come and train and hopefully in the near future something can be done.
‘So if we could get two or three more triallists in towards the end of the week it’s an opportunity for them to get 10 days in Spain for us to have a look at.’
Appleton has a number of targets on stand-by he’s ready to snap up once the Football League give him the go ahead.
But he admits the players currently hold all the power in the club’s pursuit of them.
He added: ‘The players hold all the aces until we come out of administration.
‘They have the strength. Yes they are out of contract but they are the ones wanted by the football club.
‘Hopefully, when we come out of administration we will be in a strong position because we’ll be the most attractive club they can sign for.
‘That is when I will have the upper hand and hold all the aces.
‘The problem is there are a lot who are not prepared to wait and instead have signed for other clubs. That is why I have missed out on a lot.
‘But there will be good players out there who want to leave it until the end of July.’