Forest made a cash plus player offer for Kelleher, 25, who has two years left on his Anfield deal.
Liverpool rejected the offer from Forest, just as they did in January, with Forest believed to be well short of the Reds' valuation of £35million for the player.
And Slot claims they are thinking in the short and longer term by hanging on to him and signing Giorgi Mamardashvili, who is remaining on loan at Valencia for this season.
“Maybe [he has to think of himself], but we have to make decisions as well,” said the Liverpool head coach.
“It’s not only the player. If you work at a club like Liverpool, you need competition and you need a lot of good players.
“Like I said, Mamardashvili is someone for the long-term future of the club and I’m really, really happy with the goalkeepers we have at the moment."
He added: “Caoimhin is one of them and Ali. We’re in a good place when it comes to goalkeepers for now and for the long term.”
Liverpool have landed Federico Chiesa from Juventus for an initial £10million and Slot is not expecting any more big-name arrivals.
“I’m not expecting anything, but it’s no different from all the days before,” he said. “If we see an opportunity, we could act.”
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