The 22-year-old is now into a third week on trial with the Blues as Paul Cook assesses his talents.
The Pompey boss is keen to recruit right-back cover for Drew Talbot in his squad.
Sessegnon has appeared at Sligo and Bohemians so far during pre-season and will once more be in the frame for match action against the Hawks tonight (7pm) in a strong Blues squad.
The attacking full-back last season made 38 appearances for Whitehawk in National League South, but is now bidding to crack the Football League with Pompey.
Transfer gossip: Portsmouth eye raids for ex-Chelsea man and Charlton Athletic's former Wigan Athletic midfielder
Portsmouth transfer news: Blues receive bids for former Luton and Millwall midfielder
Former Portsmouth pair help Ipswich flex muscle as Norwich City man is slammed for conduct in Peterborough's Plymouth Argyle reverse
Done deals: all the latest League One transfers including Ipswich Town, Oxford United, Bristol Rovers, Charlton Athletic and other Portsmouth rivals' business
Danny Cowley makes Portsmouth team selection admission following Cheltenham win - and gives honest assessment of current squad amid early-season promotion hopes
He actually faced the Blues during the 2014 pre-season when part of opposition Ebbsfleet.
The non-leaguers collected a 3-0 success over Andy Awford’s side at Stonebridge Road, with the Frenchman featuring for 90 minutes at right-back.
Played in front of a crowd of 879, it represented the first defeat of that pre-season under the newly-appointed permanent boss.
Now Sessegnon is seeking to clinch a south coast switch, with the Hawks representing his latest opportunity to shine.
Michael Crowe is another triallist to have remained with the Blues, having impressed in Ireland.
The Ipswich keeper is available on loan and has seen off Eric Grimes, who also featured in Ireland.
In the meantime, Cook is continuing to monitor Jamie Ashdown, who is this week training with the club as he seeks to earn a contract.
Of those players who have been injured, the Blues have received a boost, with Gareth Evans now returning to training.
The attacking midfielder sustained ankle and knee ligament damage in the second play-off semi-final against Plymouth.
However, he is unlikely to feature at Westleigh Park this evening as he continues his rehabilitation.
As revealed previously in The News, Michael Smith and Curtis Main are pencilled in to play against Lee Bradbury’s side.
Minor knocks have so far kept the pair out of pre-season action, with the duo missing both fixtures to date.
Yet they are expected to be back in the squad along with Ben Close (hamstring) for the short trip.
Cook is still continuing to monitor the fitness of Matt Clarke and Paul Jones following injury.
POMPEY (from): Crowe, Bass, Talbot, Sessegnon, Burgess, T.Davies, Whatmough, Barton, Haunstrup, Stevens, May, Close, Doyle, Rose, Roberts, Tollitt, Baker, Lalkovic, Bennett, Chaplin, Main, Smith, Clarke.