Kenny Jackett had seen a verbal offer of £500,000 for the 18-goal striker rebuffed by Peterborough.
Since then, Posh director of football Barry Fry has slapped a £750,000 price tag on the ex-Stevenage man.
That development comes after the Blues recruited Ellis Harrison from Ipswich to bolster their striking options for the forthcoming campaign.
Jackett denies Harrison’s £450,000 capture impacted on ongoing interest in Godden.
Instead Pompey’s boss insists Peterborough’s valuation dictated the end of their chase – and attention is now elsewhere.
Jackett told The News: ‘It was a verbal bid (for Godden), I phoned Darren Ferguson and discussed it with him, that was six weeks ago.
‘We haven’t put in another bid and, no, we are not going back for him.
‘We discussed it and the price was too high.
‘Moving away from Godden is not necessarily down to signing Harrison, it’s just about their valuation and where we were. Fair enough to Peterborough, I totally respect that.
‘I did phone Darren – but we haven’t visited it since then and won’t be going back.’
Harrison is earmarked for a number nine role to challenge Oli Hawkins for a place in Pompey’s attack.
A long-time target of Jackett, the Blues’ manager previously missed out on him last summer and then in January.
Pompey have not ruled out further strengthening their pool of strikers, yet the costly Godden is no longer under consideration.