Joe Cook and Ollie Dennett are hoping to win Hawks deals.
The pair both featured for the Westleigh Park outfit in their 2-0 friendly victory at Alresford Town on Saturday.
Cook featured in a centre-back role and helped Paul Doswell’s side record a clean sheet against the Wessex League premier division outfit.
The 19-year-old has previously been on the books at Sheffield Wednesday and AFC Bournemouth during his fledgling career.
He spent last term at Winchester City, while he’s also played for Poole Town.
Following the departures of Paul Robinson, Tyler Cordiner, Ryan Woodford and Jordan Rose from last season, central defence is a position that needs strengthening.
The Hawks have signed former Pompey defender Sam Magri.
Cook is also aiming to become a full-time member of Doswell's squad and the boss was impressed with his performance.
He said: ‘The two boys we have got in are Joe Cook and Ollie Dennett.
‘I knew Joe at Winchester City and previous to that he’s been at Sheffield Wednesday and AFC Bournemouth.
‘He’s only 19 and is a centre-half who is 6ft 2in. I thought he was excellent against Alresford.’
Dennett, meanwhile, was released by National League side Eastleigh earlier this summer.
The striker struggled for regular first-team minutes at the Silverlake Stadium and had a loan spell at Blackfield & Langley last campaign.
Several Spitfires players contacted Doswell recommending Dennett following his Eastleigh departure.
And with forwards Alfie Rutherford and Danny Kedwell limping out against Alresford, Doswell is set to run the rule over the 20-year-old for an extended period.
The Hawks manager added: ‘Ollie was at Eastleigh last season.
‘He didn’t get many opportunities there but a few of the Eastleigh players I know rang me up and said we should try to have a good look at him because they rate him.
‘The fact we picked up a couple of niggles with Alfie and Danny means Ollie is going to get extended opportunities.
‘We’re down to just Jonah (Ayunga) at the moment in terms of forwards.
‘So it will mean Ollie will get more game-time in pre-season and gives us a longer chance to have a look at him.’