Since arriving in Naples midway through the 2011-12 campaign, Vargas has made just 19 Serie A appearances, all as a substitute, without scoring.
The Chile international spent the second half of last season on loan at Valencia, where he was particularly impressive in their run to the UEFA Europa League semi-finals.
After holding talks with the club, Ogalde says Vargas' strong showing for Chile in their FIFA World Cup campaign has reinforced Napoli's belief that they want to keep the player.
"I spoke with Napoli on Tuesday," he told emol.com. "And the contract with them is still in force.
"They consider him an important part of the squad, and are looking forward to him starting pre-season.
"They told me that they were delighted with Eduardo at the World Cup.
"[Former coach Walter] Mazzarri didn't really like him but with [current boss Rafael] Benitz it's a different story."
