The striker reported for the first day of pre-season duty at the Blues’ training base yesterday.
Following his release from Luton, Jarvis now aims to earn a deal at Fratton Park.
But history says it will be tall order for the former Basingstoke forward to become a full-time member of Jackett’s squad.
Since taking the reins at Pompey, the boss has ran the rule over 12 players all with the same goal.
None of them were offered terms at PO4, however.
Here’s a look back at all of them and where they are today…
Turned up for Kenny Jackett’s first Pompey training session two years ago after being released from Bolton.
The boss confirmed the Blues wouldn’t be pursuing a deal after their first friendly of the summer at Salisbury.
Wilson subsequently moved to Port Vale, before dropping to the National League with Ebbsfleet.
The Chichester-born keeper trained with Pompey for several days in 2017.
He then underwent a trial period at Luton and won himself a contract at Kenilworth Road.
Yet to make his Football League debut, but did feature twice in the Checkatrade Trophy for the Hatters last term.
The Frenchman arrived on the south coast in 2017 after previously representing Servette, Lausanne-Sport and Tours.
The midfielder featured in a Premier League Cup victory over Southend before he joined Oldham.
Maouche made 41 appearances for the Latics in League Two last season.
Pompey cast their eye over the centre-back in October 2017.
He featured for the reserves against Everton under-23s but was unsuccessful in his pursuit of a deal.
The Dane subsequently crossed Stateside to join Orange County before completing a switch to SönderjyskE in his homeland in March.
The Kings Langely winger featured for the reserves against Bristol City under-23s at Privett Park in October 2017.
Karagozlu had been training with Pompey for several weeks but didn’t impress sufficiently enough to earn a contract.
Had a brief spell with the Blues midway through the 2017-18 season after leaving Leyton Orient.
The striker would go on to sign a deal at Barnsley and scored four goals in 31 appearances when the Tykes clinched promotion from League One last season.
Despite being under contract at National League side Boreham Wood, the Portuguese trained with Pompey in October 2017.
The Blues did not make a move for Andrade, though, and he’d move to Lincoln on a free transfer in May 2018.
The forward netted 11 times in 50 appearances as the Imps clinched the League Two crown last term.
Andrade has been linked with Pompey this summer.
Featured for the reserves at Leicester in November 2018, featuring for a full 90 minutes at right-back.
But Henley didn't go enough to win a Pompey contract.
He then opted for a move to MLS side Real Salt Lake but has returned to England this summer after signing a one-year deal at Bradford City.
Appeared for the reserves in a Premier League Cup clash against Leicester City at Nyewood Lane in February 2018.
The former Ipswich and Leeds midfielder has since retired.
With Pompey short of centre midfielders, the Northern Ireland international spent a brief period at PO4 in March 2018.
He’d join Plymouth for the remainder of the 2017-18 campaign, making three appearances.
Paton spent last season at Falkirk before making the switch to rivals Dunfermline Athletic this summer.
Trained with Pompey towards the end of the 2017-18 campaign.
The Chelsea midfielder impressed Kenny Jackett – but didn’t try to make a swoop.
Sammut had a spell on loan at Falkirk last term before being released from Stamford Bridge this summer.
The keeper a brief period with the Blues in January while Luke McGee was out injured.
However, the former Burton Albion man left for Accrington after he was offered a contract at the Wham Stadium.