And The News understands Pompey are hopeful of reaching agreement with Manchester City over a season-long loan.
The 19-year-old shone during a similar arrangement with Rochdale last season, making 32 appearances in all competitions.
Manchester City are keen to once again find matches for the Republic of Ireland international to aid his development.
That has alerted Pompey, who presently favour Bazunu ahead of another target in West Brom’s Josh Griffiths.
Alex Bass is currently the only goalkeeper on the Blues’ books, with Cowley a fan of the 23-year-old.
Yet Cowley wants competition for his number one spot – with Bazunu highly regarded by the Premier League Champions.
The Irish keeper is contracted to Manchester City until the summer of 2024 and has represented his country on four occasions.
The teenager’s most recent Republic of Ireland appearance was in June’s goalless draw with Hungary in a friendly.
Bazunu started that match before replaced at half-time by Liverpool’s Caoimhin Kelleher, while Pompey’s Ronan Curtis was an unused substitute.
The Blues are on the hunt for a goalkeeper following the end-of-season departures of Craig MacGillivray, Duncan Turnbull and Taylor Seymour.
Pompey are also currently without a goalkeeping coach after the long-serving John Keeley was not retained.
He has since linked up with Ipswich, reuniting with Paul Cook, his former Fratton Park manager.
Meanwhile, another Pompey goalkeeper target, Griffiths, is available for loan from West Brom after last season making 50 appearances for League Two champions Cheltenham.
A message from the Editor, Mark Waldron
The News has launched a subscription offer which gives you unlimited access to all of our Pompey coverage, starting at less than 14p a day.
You can subscribe here to get the latest news from Fratton Park - and to support our local team of expert Pompey writers.