It is understood the keeper is on Boro’s radar following his promising breakthrough season at Fratton Park.
Bass enjoyed a fine campaign for the Blues after dislodging Craig MacGillivray as first-choice keeper at Gillingham on New Year’s Day.
In total, the academy graduate made 25 appearances, recording eight clean sheets, while his save percentage ratio was better than any other stopper in the top four divisions.
The move could generate the kind of funds to allow Kenny Jackett to overhaul his squad following Pompey’s League One play-off semi-final defeat to Oxford.
Bass, 22, is under contract at Fratton Park until the summer of 2023, after penning a new three-and-a-half deal back in January.
It, therefore, puts the Blues in a strong bargaining position to maximise a return on his talent should they decide to cash in.
Now Middlesbrough have emerged as another club to test their resolve.
Neil Warnock has been appointed permanent boss at the Riverside, having taken over in a caretaker capacity following the sacking of Jonathan Woodgate in June.
Warnock has said he plans to take Boro to ‘the other end of the table’ next season, after a disappointing 17th-place finish in the Championship, and is targeting a ‘large influx of players’ during the transfer window.
The Teeside outfit sold Republic of Ireland international goalkeeper Darren Randolph to West Ham in January and have arguably not replaced him.
In the final few weeks of the season, Aynsley Pears and Dejan Stojanovic battled it out for a starting spot.
That suggests Warnock may want a keeper who will feature week in, week out.
Boro have also recently been linked with Dillon Phillips following Charlton's relegation to League One.
Pompey are currently well stocked in the goalkeeping department.
Before his shock omission at Gillingham, MacGillivray featured in every league game he was available for following his arrival from Shrewsbury in June 2018.
The Scot quickly established himself as a fans’ favourite shortly after joining the club and helped the Blues win the Checkatrade Trophy at Wembley.
Boss Jackett explained it was a ‘gut feeling’ why he dropped MacGillivray for Bass at Gillingham.
American Duncan Turnbull is currently third-choice keeper and under contract until 2021, with a club option for an additional 12 months.
A message from the Editor, Mark Waldron
Thank you for reading this story. The dramatic events of 2020 are having a major impact on our advertisers and thus our revenues.
Every subscription helps us continue providing trusted, local journalism and campaign on your behalf for our city.