Accrington’s Colby Bishop and Cardiff’s James Collins were the latest names added to that list this week.
And while there’s hope a deal can be struck for the former, Pompey are already giving up hope of bringing the latter to Fratton Park.
But what about those other attackers rumoured to be on the Blues’ radar?
What’s happened to those prospective moves? Where are those players now?
Well, we’ve revisited them all to find out whether they can still come true, whether they’ve been consigned to the rumour mill bin or whether other clubs have since come in to ruin the Blues’ plans.
1. Cole Stockton - Morecambe
The prolific Morecambe front man was linked with the Blues even before the final whistle blew on last season. According to reports back then, Preston, Peterborough, Rotherham and Wigan were all keen. But talk of a move anywhere for the 28-year-old has since dried up and, at present, he looks set to remain with the Shrimps. Picture: Julian Finney/Getty Images Photo: Julian Finney
2. Kyle Wootton - Notts County
Pompey had a long-standing interest in the Notts County front man, with Cowley admitting he had travelled on numerous occasions to watch the striker in action. Pompey's interest soon cooled, though, before the lure of a move to League Two Stockport saw Wotton eventually leave Meadow Lane. Picture: Lewis Storey/Getty Images Photo: Lewis Storey
3. Aaron Collins - Bristol Rovers
The Bristol Rovers front man fits the bill in terms of the profile Danny Cowley wants this summer - young, talented, energetic and with bags of potential. However, Collins quickly made it known that he was keen to remain with the Gas for their return to League One. His decision to stay at the Memorial Stadium will see him link with former Pompey striker John Marquis next season. Picture: Harry Trump/Getty Images Photo: Harry Trump
4. Brandon Thomas-Asante - Salford
The 23-year-old Salford striker was being touted for a move to Pompey this summer as far back as March. Those links have continued, with MK Dons, Ipswich, Wigan, Swansea, Cardiff and Reading also reported admirers. He remains at Salford, with a move to Fratton Park looking highly unlikely. Picture: Nathan Stirk/Getty Images Photo: Nathan Stirk