"I've played a lot of games now as well and shown my level. The next step for me is to be playing week in, week out and every week.
"There was some interest. It's normal when you play for a club like Liverpool - and I obviously had a long spell in goal last season and thought I did quite well.
'When you play for Liverpool other teams will be interested in you'"It comes hand in hand that when you play for a club like Liverpool then other teams will be interested in you."
The problem for Kelleher is that interest manifested itself in bids more appropriate for untried reserve keepers than those with his big-game experience. In a world in which Southampton paid PS25 million for Arsenal back-up Aaron Ramsdale, Liverpool stood firm on demanding similar for Ireland's No 1. In a sense, Kelleher's excellence made his transfer less likely.
"I think that's a good point. It does work both ways," he says.
"I played so many times last season and if you do well your valuation goes up. Obviously the club is going to want to get a good profit. But like I said before, there are a lot of opportunities here too.
"I spoke with the manager about the situation - but I was quite clear before he came in and it was never going to change because the fact is that I am up against Alisson and he's one of the best in the world, so he's always going to be No 1 and he's always going to play.
"There were other factors, like negotiations with clubs as well as Liverpool needing to be happy. At the end of the day, it just didn't materialise and I didn't get a move."
Liverpool's PS30 million deal for Georgian keeper Giorgi Mamardashvili - he will join next summer - was a further blow to Kelleher's hopes of becoming Allison's long-term successor.
"No, there were no conversations [about Mamardashvili signing]. That's next summer. I am not thinking about that right now. I just want to do as well as I can in these coming games," says Kelleher.
So are the next six weeks a chance to attract more realistic offers?
"I am not looking at it as anything other than I have an opportunity to play a few games, so I want to do as well as I can," says Kelleher.
"There is no point making this a bigger picture than it is. It is just me getting the opportunity to play some games.
"I am good mates with Ali [Allison]. We are close so I sent him a text to say sorry about the injury. It is not nice for him and I don't like to see that happen to anyone.
"It has been beneficial for me training with someone of such high quality. You obviously learn from that and it brings you on.
'The best thing I can do is go and play well'"Obviously the team is doing quite well, I want to help keep winning in the league and the Champions League. That is my main ambition - to help the team and help myself by doing well.
"That is where my head is at with the situation. The best thing I can do is go and play well and, yeah, maybe give the manager something to think about, give him a headache maybe. If I play so well, how can he take me out, something like that. Do as well as I can to put some pressure on at least.
"There is going to be frustration not playing week in, week out. But I still need to be ready. I have been professional and always will be, because if I am not ready I am not doing myself justice. I need to give myself the best chance to play as well as I can."
Chelsea are appropriate opposition for a first-team comeback, given that Kelleher shone in two Carabao Cup final victories against the Londoners.
"It's been brilliant every time I've played them, to be fair," he says. "Two finals as well. Happy memories. Hopefully there will be more."