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AFC Wimbledon boss Neal Ardley insists he is committed to the League 2 side.
Gillingham are believed to have made an official approach to speak with Ardley about their management vacancy.
The Gills have been without a boss since chairman Paul Scally sacked Peter Taylor on New Year’s Eve.
Speaking after the Dons lost to Carlisle on Saturday, Ardley said his club have refused the Gills permission for him to talk.
"They've done it the proper way and approached the club," said Ardley.
"I'm very pleased the club don't want to lose me - and I don't want to go.
“I’m fully committed to this club. This club gave me my first chance and from my point of view I’ve not got it where I want it to be. I’ll endeavour to do that and work hard.
“We’ve had a decent season so far with cup runs, but we now need to focus on getting into the top-10.”
Ardley was named as League 2 manager of the month for December and his Wimbledon team earned rave reviews following their narrow defeat to Liverpool in the FA Cup.
The 42-year-old has previously played for Wimbledon, Watford, Cardiff and Millwall.
He has been manager of Wimbledon since October 2012. His team are currently 13 in League 2.
The Gills ended a run of three straight defeats under their caretaker management team with a 3-1 win over Coventry City on Saturday.
Mr Scally is already conducting interviews for their vacancy and the Gills were linked with a move for Newport County boss Justin Edinburgh last week.
But their outgoing chief executive Dave Boddy doesn’t believe the Essex-based boss will be joining the Gills.
Speaking before the weekend, he said: “I think everybody at the club is fairly confident that Justin will still be manager after the Gillingham managerial process is over.”
Former England striker James Beattie said last week that he was interested in the job.