Steve Cotterill admitted he was ‘hopeful’ rather than confident of bringing in more recruits before the pre-season tour to America.
The Blues fly out on Sunday morning for 12 days in North and South Carolina.
In the meantime, Cotterill continues to pursue a number of targets to add to the five new faces already brought to Fratton Park this summer.
A striker, central defender and left-back are just some of the positions which require strengthening for a squad which, at present, numbers 15.
Martin Paterson and Paul Konchesky are continually being linked with prospective moves to Pompey.
But after a flurry of transfer activity last week, Cotterill is uncertain whether more faces will be arriving during this week.
He said: ‘Are we going to get in anyone this week? I don’t know the answer to that one.
‘I can only say I’d have to be hopeful.
‘I wouldn’t be over-confident.
‘We are looking at buying players at the minute.
‘There are no more free transfers out there we would bring in who we could either afford or would perhaps be the type we would want to bring to the club now.
‘It is probably down to bids and them being accepted.
‘We haven’t got a large team at the moment so we still need to do some work on that.
‘The new owners have come in and been absolutely first class with me so far.
‘They have been really, really supportive.
‘But it is difficult because we have again lost another summer of free transfers.
‘It means it costs a little bit more money to put the squad together.
‘But we will do our best.’
In a busy past fortnight, Pompey have so far recruited David Norris, Stephen Henderson, Greg Halford, Luke Varney and Jason Pearce.