Reports emerged earlier that the Blues forward had entered talks with both the Owls and Plymouth over a potential PO4 exit.
However, a switch to Hillsborough now appears highly unlikely with heightened speculation former West Brom striker Saido Berahino is set to reunite with his ex-Baggies boss Darren Moore at Sheffield Wednesday.
Reports from Belgium suggest Zulte Waregem forward Berahino, 28, will sign for an unnamed English club on deadline day, which is believed to be the Owls.
The highly rated former Baggies ace made the breakthrough at the Hawthorns and was linked with a move to Premier League heavyweights Tottenham and Liverpool earlier in his career.
Should the Owls pull a deal off, it would likely mean Hillsborough is not a possible destination for Harrison.
Instead, Harrison was at the club's Hilsea training base going through an individual session.
The News understand Pompey are willing to offload the front man before this evening's transfer deadline.
But it now appears Sheffield Wednesday will not be his destination should he leave with Berahino believed to be close to joining the Owls.
Bristol Rovers, Oxford United and Plymouth are all clubs who are believed to remain keen on making a deadline day move for Harrison.