The 20-year-old is bidding to impress Kenny Jackett during a week-long stay with the Blues
Wood, who is a free agent, has been flagged up to Pompey as a talented winger, capable of playing on either flank.
He actually featured against Pompey in July, coming off the bench as a triallist for Woking in the Blues’ 4-2 pre-season victory.
Last term he turned out for Walton Casuals, making 31 appearances and scoring once for the Evo-Stik Southern Premier League side.
During the campaign, he was also loaned out to Herne Bay and Molesey, while reportedly was offered a trial by Charlton.
Jackett said: ‘Nathan did his apprenticeship at AFC Wimbledon and was with Woking earlier this season.
‘He is a winger, right or left, and we’re just having a look at him and seeing how he does.
‘We’ve already seen him play against us in pre-season, he came on as a substitute for Woking.
‘Nathan is somebody who has been flagged up and we are happy to have a look at him this week.’
Former Norwich and Bromley right-sided player Richard Brindley continues to train with Pompey, as does James Meredith.
Jackett added: ‘Brindley is still training with us and is 100 per cent looking for a club.
‘If it gets around to the Premier League Cup next week, we will go as strong as possible for our game at Doncaster and he can help us as well.
‘It works both ways – he is benefiting and helping the squad too.’