The club's talks with manager Abbott, assistant Kavanagh and coach Caig over new deals are near completion.
Nixon said no approach had been made by Hartlepool to speak with Kavanagh about the current manager's vacancy at Victoria Park.
"All three members of staff have had their offers and the indication is that they all want to announce their agreement together," Nixon told Carlisle's official website.
"There are one or two items up for discussion, but I don't think there is anything too significant in there.
"It's all standard for this kind of thing and we're expecting to hear back very soon."
Former Middlesbrough, Stoke and Cardiff midfielder Kavanagh, who joined up with Abbott at Carlisle as player/coach in January 2009, was last week installed as an early favourite to replace the sacked John Hughes at Hartlepool.
But Nixon added: "Graham is under contract until the end of June and, as far as we are concerned, he is now in the process of agreeing to a one-year extension to that.
"With that in mind, and with the type of character he is and the excellent working relationship we have with Hartlepool, I have no doubt that both parties would have contacted us had there been any substance to these stories and rumours.
"We have had no contact at all about this issue which tells us that they are, in fact, just stories and rumours."