The News understands the Bristol City man is a player being considered by Kenny Jackett in the January window.
Szmodics is available on loan after failing to make the first-team breakthrough at Ashton Gate after signing from Colchester in the summer.
But the Blues face stiff competition from the likes of Championship pair Hull and Huddersfield for the 24-year-old’s signature, along with League One rivals Ipswich.
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And Szmodics is a player who has been mentioned as an option in the midfield area, with the Blues boss keen for recruits who can make an immediate impact in their bid to reach the Championship.
The direct runner and goal threat joined the Robins on a three-year deal this summer, but has been restricted to 107 minutes of league action with a 72-minute runout in his side’s Carabao Cup defeat to QPR.
Szmodics came through the ranks at Colchester and added an increasing cutting edge to his game, bagging 13 League Two strikes in the 2017-18 season before delivering a 15-goal return last term.
Pompey yesterday landed left-back Steve Seddon on loan from Birmingham for the season, as Jackett moved quickly to bolster his options after the January window opened.