The Manchester City youngster is top of the Blues head coach’s goalkeeping targets as he plots a renewed League One promotion push.
Alex Bass is the only senior stopper under contract following the departures of Craig MacGillivray, Duncan Turnbull and Taylor Seymour.
Cowley wants someone to come in to challenge the academy product for a starting spot.
Bazunu’s been identified as Pompey’s chief target, having spent the 2020-21 campaign on loan at Rochdale.
The 19-year-old made 33 appearances for the Dale as they were relegated from the third tier, while he also broke into the Republic of Ireland senior set-up.
To get more on Bazunu’s Spotland spell, we spoke to David Chaffey, writer and podcaster for rochdaleafc.com.
How did Gavin Bazunu fare during his loan spell at Rochdale?
He is extremely highly rated in the game and arrived at us aged 18, which is young for a goalkeeper.
We saw a lot of inexperience and, in all honesty, may not go down as a loan signing successful among Rochdale fans.
He played 32 games but we conceded 61 goals. It was difficult because he had a lacklustre defence in front of him, which never helps when you're that young for a keeper.
It was always going to be a difficult season as we were favourites for relegation.
That's not saying Bazunu doesn't have plenty of good attributes. His reflexes are really good, he's a really good shotstopper.
His distribution probably needs work, as does commanding his area, but he is a wonderful prospect and very highly thought of.
He made a few mistakes but I'm not surprised by that given his age and the pressure he'd have been under.
There is certainly a good goalkeeper in there and he'll go on to have a very good career.
When he joined Rochdale, were you surprised to have signed someone of Bazunu's ilk?
We've had a bit of an agreement with Manchester City for a little while. They see us as a club that can help develop their players.
We also got centre-back Yeboah Amankwah but he picked up a season-ending injury very early on.
It wasn't a surprise we got someone from Manchester City but it was we signed Bazunu. I have friends over in Ireland who told me about him before and he's very highly rated.
It looked like a really good signing on paper but he was a bit of a mixed bag.
Danny Cowley wants a keeper good with his feet. You mentioned Bazunu's distribution needs work?
Rochdale did play out from the back quite a lot and he's fine with that aspect of it.
His kicking needs improving. When we did go a bit longer, his kicking was brilliant and decision-making could be a bit naive.
There was one example at home to Oxford. We were drawing and the ball came to him in the last minute but rather than putting the ball out into touch, he kicked it straight to an Oxford player, who went on to score.
Bazunu can play out from the back and most keepers at Premier League clubs are coached to do that from an early age.
He will be a lot better having a season at Rochdale for his own development. He'd have experienced a lot he wouldn't have got at youth level with Manchester City.
I'd suspect Bazunu will have a better season with Pompey than with us.
Did you expect him to be called up to the Republic of Ireland senior squad?
It was a bit surprising given what we'd seen of him. He's been a regular for the under-21s so the natural progression is getting him involved into the senior squad as quickly as possible.
Fair play to him, I was pleased to see him get international recognition.
After Pompey beat Rochdale 2-0 on April 2, Bazunu didn't play again. Why was that?
Brian Barry-Murphy said he wanted to give Bazunu a rest then performances picked up when Jay Lynch was in net and became first choice.
Lynch did nothing to warrant being dropped and Bazunu probably did need a bit of a rest in terms of mental fatigue. To be expected to play all season in a relegation dogfight aged 18 is asking an awful lot.
I'd imagine it would have been fine with Manchester City. He'd played a lot in effectively his first professional season and you'd think it was agreed with both parties.
Is a promotion-challenging League One side the next natural step in his career?
A club like Pompey is the natural step. He will be massively helped by being at Rochdale last season for his development.
With a better defence in front of him, he would be a good acquisition for Pompey.
He will need nurturing. He's raw but got a lot of really good attributes.
Some of the saves he pulled off were magnificent but maybe struggled with some of the mental sides of the game.
I think Danny Cowley can use Bazunu a bit better than Rochdale. He's not going to be under as much pressure compared to when you're getting beat every week because that's going to hamper a goalkeeper's confidence.