The boss attended a UEFA coaching forum earlier this week before paying a visit to relatives in Liverpool, sparking rumours that the Spaniard has a strained relationship with De Laurentiis.
However, the club said: "Reports today in some newspapers that Benitez taking a few days off is another sign that the relationship with De Laurentiis has 'cracked' is not only false but ridiculous.
"The relationship between the coach and the president of Napoli is excellent as they themselves have repeatedly stressed.
"As already announced, Rafa Benitez took a few days off, after being in Nyon for the regular meeting between the coaches of the most important teams in Europe, to be reunited with his family in Liverpool. Benitez will return to Naples on Wednesday to resume the coordination of training on Thursday to coincide with the return of many absent national players, four days before the match with Chievo."
Prior to the international break, Napoli were knocked out of the Champions League by Athletic Bilbao.