The Blues youngster – who is currently on a season-long loan from Manchester City – served up his 15th shutout of the season in Saturday’s goalless draw at Ipswich.
But with Liverpool No2 and Carabao Cup hero Caoimhin Kelleher breathing down his neck and Bournemouth ace Mark Travers – whom Kenny stated has ‘had the best season’ out of the trio – also knocking on the door, Bazunu knows there’s more at play than meets the eye.
Indeed, with Ireland’s coaching team watching every game and taking note of what they’ve seen, the Dubliner is fully aware that every display counts.
The Pompey keeper produced a couple of fine saves in Saturday’s stalemate at Portman Road to keep those watching eyes suitably impressed.
Yet he went into the game on the back of a poor goal conceded in the 3-1 win at Crewe just days earlier.
The latest Republic of Ireland squad is expected to be named next week ahead of friendlies against Belgium (March 26) and Lithuania (March 29).
Barring injury, first-choice Bazunu will be in those squads and will add to his 10 caps for his country.
But he knows simply keeping clean sheets for Pompey in League One won’t keep him there.
Speaking to The News about the upcoming internationals, Bazunu said: ‘It’s not just the clean sheets they (Kenny’s team of scouts) are looking at, it’s the performances, too.
‘The performances are key because they have people looking at every game so I’ve just got to keep these solid performances going.’
Bazunu’s Ireland involvement – plus potential call-ups for Joe Morrell (Wales) and Ollie Webber (Northern Ireland under-21s) – will likely see Pompey’s game at Bolton on March 26 postponed.
That means an enforced break is on its way for Cowley & Co, with the League One fixture against Rotherham on April 2 having to be rearranged because of the Millers’ involvement in the Papa John’s Trophy final on the same day.
In the meantime, Ireland boss Kenny is delighted with the options he has heading into the international break.
He said: ‘When you meet Gavin for the first time in a group, he is a leader and has leadership qualities.
‘He is just someone who carries himself with this sort of aura.
‘He would have done well in life whatever he had done. He has a presence, has a sort of unflappable nature that is incredible for one so young.
‘He has obvious inbuilt character traits that give you the capacity to give away a penalty but then save it in the same vein.
‘You never underestimate Caoimhin.
‘He played for me in the under-21 team, he played 10 of the 12 internationals. He was the one who played most for me.
‘He’s laconic, makes goalkeeping nearly an art form. It’s beautiful to watch him, aesthetically amazing to watch.
‘We have three keepers. Mark Travers, he has had the best season.
‘Probably because Gavin is playing in League One, you wouldn't consider that he's had the best season.
‘Mark arguably has had in terms of whether you measure Caoimhín winning the trophy.’