Pompey have had a £2.5m bid rejected for Martin Paterson.
It is the latest blow for Steve Cotterill in his dogged pursuit of the Burnley striker he rates so highly.
The Blues have had a number of bids rejected for the 24-year-old over the past six weeks.
But the Clarets cannot be tempted to do business.
It now appears Cotterill will have to look elsewhere as he urgently seeks to strengthen his striking ranks.
Pompey had already been losing hope of persuading Burnley boss Eddie Howe to part with Paterson.
This latest setback may now convince them to shut the door and move on.
Cotterill has made no secret of the fact he would like to bring two strikers to Fratton Park this summer.
He had earmarked Paterson as one of them, a player he feels could be a massive hit at Fratton Park.
Former Stoke man Paterson scored 19 goals in the season the Potters won promotion to the Premier League.
He has suffered injury problems since that impressive 2008-09 season .
But Howe still rates Paterson highly and is loath to sell him, particularly in light of allowing Chris Iwelumo, Chris Eagles and Tyrone Mears to leave Turf Moor this summer.
It appears Pompey must now set their sights elsewhere, with the prospect of upping their bid looking increasingly unlikely.
Cotterill has been handed a transfer kitty by owners Convers Sports Initiatives.
However, he is well aware that must stretch to bringing in a host of players to bolster his small squad.
Although a striker remains his priority, Pompey’s boss also wants a versatile defender and a central midfielder.