The Doncaster Rovers forward was left out of the match-day squad for his side’s goalless draw against the Blues last weekend as they look to get him off their books.
Donny boss Richie Wellens is bidding to offload Bogle in order to bring in a 'renowned League One striker' they have reportedly lined up.
However, Bogle, 29, who netted four times in 14 appearances for Pompey during a loan spell at PO4 in the second half of the 2018-19 season, was not interested in either of the options available to him from what were believed to be two League Two clubs.
Bradford were reported to be the frontrunners to become Bogle's ninth different Football League club.
But boss Wellens has told how neither of the two offers available to him to leave the Keepmoat Stadium appealed to Bogle.
Speaking to our sister title, The Doncaster Free Press, Wellens said: ‘I think the couple of clubs that have asked about Omar don’t take his fancy.
‘I don’t think that is going to go anywhere.
‘These players have had maybe three months to find another club and it’s not happened.
‘I have to at the back of my mind think that it’s not going to happen.’
Bogle was brought to Fratton Park on loan from Championship side Cardiff by former Blues boss Kenny Jackett in January 2019.
The striker became an instant hit at the club, netting in his opening two Pompey appearances.
However, Bogle would go onto strike just twice more in his following 12 appearances for the Blues as they suffered a semi-final play-off defeat at the hands of Sunderland to miss out on promotion at the end of that campaign.
Pompey did not pursue a permanent deal for the forward in the summer of 2019, with Bogle eventually joining Dutch side ADO Den Haag following his Cardiff exit.
The Blues and the Bluebirds are just two of EFL clubs the well-travelled striker has featured for, with spells also coming at Grimsby, Wigan, Peterborough, Birmingham, Charlton and current club Donny.