Kenny Jackett revealed Oli Hawkins has attracted transfer enquiries.
But the Blues boss wants to keep the striker whose Wembley penalty secured the Checkatrade Trophy.
Hawkins is presently sidelined for up to seven days, having suffered soreness to the instep of his foot.
It piles more agony onto the 27-year-old, who has endured a miserable summer blighted by injury and then losing his place in Pompey’s squad.
Following a back injury, Hawkins’ sole friendly outing was at Woking, netting twice in a 4-2 win.
Subsequently, he failed to make the Blues’ 18-man squad in their opening two League One matches, although was an unused substitute in the Carabao Cup.
And, ahead of the September 2 transfer window, Jackett admitted interest in the ex-Dagenham & Redbridge man had been received .
He said: ‘There have been one or two enquiries for Oli, but no offer.
‘We’ll see if it actually gets to that stage for me to then speak to the player. There have been no offers.
‘You can put a level of enquiry in, maybe a manager who knows me might phone me, while recruitment teams talk to each other all the time.
‘Mark and Tony might get their opposite numbers on the phone – but when it gets to their level usually it is serious stuff.
‘A manager, coaching staff, recruitment staff, that is what I deem an enquiry.
‘If it gets to Mark Catlin or Tony Brown, that’s an offer.
‘Oli is someone I definitely want to keep, I am keen to see how he responds and if he can fight back.’
Hawkins netted 10 goals in 48 appearances last season as he established himself as the focal point of Pompey’s attack.
The Blues were the highest-scoring team outside the Premier League, with the striker’s hold-up play and ability to create opportunities for others pivotal.
However, the expensive summer acquisitions of John Marquis and Ellis Harrison have restricted Hawkins’ involvement during the current campaign.
Jackett added: ‘Oli has been okay.
‘He is disappointed to be out of it, but understands this is Portsmouth Football Club and in the summer they may sign a centre-forward – and that’s what has happened.
‘We signed a couple in the summer of 2017 – which was Brett and him – then, in terms of last season, he’s had a clear run at it from the start and done well.
‘Now we have again invested as we’ve brought some money in through Jamal Lowe and Matt Clarke.
‘We have invested in some fresh forwards – and that is competition.’