The attacking midfielder has swiftly fallen out of favour under the Championship club’s new boss, Gerhard Struber, since his mid-November appointment.
And that has alerted the Blues to the 24-year-old’s availability on a loan deal for the remainder of the campaign.
Should they succeed in capturing him, it would represent a massive statement of intent in terms of promotion ambition.
McGeehan scored six goals in 44 matches last season as Barnsley finished second in League One to earn promotion.
He started both games against Kenny Jackett’s side during that campaign, each ending in draws.
The former Norwich man was subsequently handed a new two-year deal by the Tykes in June and has made 14 appearances this season, including 10 starts in the Championship.
However, since Struber’s Oakwell appointment, McGeehan has featured just twice, not making the last five squads.
McGeehan had an unhappy visit to Fratton Park in January 2017, when he broke his leg while representing Luton.
The midfielder’s reaction while injured on the pitch then earned him booking from referee Tim Robinson.
Pompey have already recruited Steve Seddon on loan from Birmingham, while Reeco Hackett-Fairchild today joined for an undisclosed fee from Bromley.