The 29-year-old, who has made 26 appearances for the Cumbrians this season, could leave Brunton Park for the Ladbrokes Premiership after Killie manager Gary Locke approached the Sky Bet League Two club.
United boss Keith Curle told carlisleunited.co.uk: “I’ve spoken to the Kilmarnock manager about Gary and we had a good conversation.
“I’ve now given the player permission to talk to them and we’ll see what comes of that.”
Dicker joined Carlisle from Crawley in 2014 having previously enjoyed a year with Rochdale after four seasons with Brighton. He won promotion to the Championship with the Seagulls five years ago.
Locke is also reportedly interested in Crystal Palace striker Sullay Kaikai and Sheffield United right-back Kieron Freeman as he looks to bolster his squad in a bid to get away from the relegation zone.
The Ayrshire side are currently in the play-off spot albeit only one point behind the three teams ahead.
Kilmarnock assistant coach Peter Leven, talking ahead of the home Ladbrokes Premiership game against Hamilton on Saturday, spoke specifically about Dicker.
“He is obviously one that we have identified so we will just need to see what happens,” said the former Kilmarnock, MK Dons and Oxford midfielder.
“There have been a few. Gary Dicker, obviously I know, I played against him a good few times down south. He is a good midfielder.
“So we have spoken to a few players and it would be nice to get a couple in, just to have fresh faces in the changing room and to try to improve the squad.”
Leven acknowledged Kilmarnock’s perilous position following the 5-1 thumping by bottom side Dundee United at Tannadice on Saturday which narrowed the lead over the Terrors to 11 points but insists “there is a long way to go”
He said. “We are just over the halfway mark. A good few wins under our belt and we could be climbing that table.
“We just didn’t turn up for the first half and every shot on goal went in.
“But we have to move on, we don’t dwell on it. We have a big game on Saturday.
“In this league anybody can beat anybody. We can go to St Johnstone who are sitting fourth in the league, and win and draw against Celtic at Parkhead.
“We just need to make sure we are up for it, the way we are against St Johnstone and Celtic and teams like that.”
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