The 23-year-old Uruguayan international, who impressed in his country's run to the semi-finals at the World Cup in South Africa, joined the southern Italian giants from Sicilian side Palermo on loan this summer.
GEAR:Save 10% on Liverpool home, away and third kits here, courtesy of Kitbag
But the former Tottenham target has already been the subject of speculation linking him with a €17-million move to Anfield.
According to reports in the Italian press, Liverpool boss Roy Hodgson is poised to launch a bid to bring the striker to England as a partner for the mis-firing Fernando Torres, but the claims have been dismissed by Anelucci.
"An offer for Cavani? These are only fantasies because Liverpool have not reached any deal,” Anelucci told Italian website tuttomercatoweb.
“Edinson is fine in Naples, he is doing well at the club and is getting on very well with everyone.
"There are no problems and this is not the time for the transfer market."
Anelucci also moved to dispel rumours that Cavani's only motivation behind the move to Naples was to use the Azzurri as a stepping stone to a bigger club.
"Napoli is an end point and not a springboard for Cavani," insisted Anelucci.
"And any bid should not come to us but to Napoli and they will decide what to do. But I don't think the club should be deprived of Edinson."
So far this season, Cavani has bagged an impressive five goals from six games in Serie A and is set to line up against Hodgson's transitional Liverpool side in the group stage of the Europa League this month.
By James Martini
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
