Barnsley have admitted defeat in their bid to snap up Kelvin Etuhu.
And Oakwell chiefs believe the free agent is set to remain with Pompey instead.
The midfielder this week held talks with Tykes boss Keith Hill over a switch to the Championship side.
Michael Appleton is also keen to keep hold of Etuhu and has tabled a two-year bid.
And Barnsley director Don Rowing thinks Pompey will emerge as the destination for the 23-year-old.
He said: ‘We have spoken to Kelvin and his agent and put an offer to them, but it is looking increasingly like he will be staying with Portsmouth now.
‘We’ll see how that one develops but it isn’t looking overly promising.’