Ipswich have made an improved offer for Joel Ward and Jason Pearce.
Sources in Suffolk say the Tractor Boys are still on the trail of the talented young Pompey duo.
The Blues rejected a bid for the pair, thought to be in the region of £1m, last week.
But that hasn’t put off their Championship rivals who remain keen, with Leicester also said to be in the frame.
Michael Appleton is expecting to be told he will have to further reduce the smallest squad in the Football League, in the wake of the club being left with an unpaid £1.6m tax bill.
Speaking last week, Ipswich boss Paul Jewell intimated his club would return for Ward and Pearce.
He said: ‘I’ve never been manager of a club that’s accepted a first bid and I’ve known a first bid to be accepted by any selling club.
‘We’re all guilty of it. You always put a higher valuation on your own player and a lesser one on an opposition player.
‘If we can do it, we’re interested, if we can’t, we move on.
‘I don’t know what their valuation is.
‘We’re competitive, there’s no doubt about that, but everyone has to have a price.’