As revealed by The News on Friday, the 31-year-old free agent is presently training with the Blues on a trial basis.
With Lee Brown ruled out of action for up to six weeks through an Achilles injury, it leaves Brandon Haunstrup as Pompey’s sole natural left-footer.
That situation has prompted Jackett to run the rule over Meredith, who has been training since Friday.
And the Blues boss believes the former Millwall and Bradford left-back possesses the talent to enhance his squad.
Ronan Curtis' Portsmouth future spelt out by trusted source well in the know - with advice on where to play Irishman added, too
Former Portsmouth keeper Alex Bass suffers tough night on and off the pitch as he makes Sunderland debut following Fratton Park exit
Portsmouth's Miniesta bidding to live up to big reputation - and those comparisons with ex-Barcelona and Spain star
'We wanted to show him a bit of love' - Portsmouth-based Spurs fans' terrific gesture to ensure Dane Scarlett feels at home on the south-coast
The most expensive estimated League One combined XI - including two Portsmouth, four Barnsley, one Oxford United and two Derby aces
Jackett said: ‘Meredith is a player that has played a lot of league games, mainly in the left-back spot, but could quite easily play wide left as well.
‘I am aware we are now down to one natural left-footer, hence the trial for him.
‘He played 36 Championship games last season and has a good pedigree as well. He’s someone I’ve seen do very well for Millwall and Bradford down the years.
‘It will be interesting to see how he goes. Obviously it has been brought about by the Lee Brown injury, but I do think natural left-footers are something you need in a group.
‘We are going to have a look at Meredith in training. I don't think a decision is necessarily imminent, he has done two days and hasn’t done any pre-season.
‘He trained on Friday and Monday – and we will certainly look at him all this week and see where we are.
‘He has done fine, is a terrific pro, has good athleticism and is an experienced player who knows what is needed in terms of training, approach and attitude.’
Meredith left Millwall under a cloud this summer, with his contract cancelled by mutual consent.
Intriguingly, his departure came following 33 Championship starts last term, as the Lions finished one place above the relegation zone.
His maiden season at The Den, in 2017-18, saw the Australian international establish himself as an ever-present in their league campaign.
Previously, Meredith won League Two promotion with Bradford, while later lost in the League One play-off final to Millwall in May 2017.
That summer he did reach the Championship, however, moving to Neil Harris’ newly-promoted side.
Jackett added: ‘I’m don’t know why Meredith left Millwall, it isn’t anything I have necessarily looked into.
‘He is where he is now. He’s living in London and has been waiting either for a Championship club or perhaps a move abroad, because he is Australian.
‘Sometimes they don’t come off – and we are happy to have a look at him.’