Pompey will have to smash the £1m barrier to land Mo Eisa.
Peterborough director of football, Barry Fry, has revealed his club had a bid of that amount turned down for the in-demand striker.
Kenny Jackett is keen on bringing in the hitman, who Cheltenham have put a £1.5m valuation on.
That's with Conor Chaplin's future in doubt and Coventry leading a number of clubs interested in landing the 21-year-old.
Pompey would have to spend big, though, to bring in Eisa as Chaplin's replacement.
A host of Championship sides are said to be interested in the 23-year-old.
Fry told the Peterborough Telegraph: 'We bid a million pound for Eisa and we couldn’t believe it when it was turned down, but his agent said he has a Championship club interested so good luck to him.
'We’ve been chasing Eisa since he ran us ragged in a friendly last summer, but we haven’t managed to pull it off. We should have brought him back with us after the game in Cheltenham.
'It’s been a difficult market recently. We have lodged several bids for several players, but nothing is moving. The manager wants more players and we are trying our best for him.
'I’d have thought with the transfer window closing earlier this season clubs would have got on with their business. Many clubs have to sell before they can buy and others are struggling with financial fairplay, but we are in the market for new players.'