The 33-year-old will be out of contract at the Stadio San Paolo this summer, although the enforced football shutdown due to the coronavirus pandemic has created further uncertainty over what his situation will be on July 1.
Aston Villa and Sevilla have previously been linked with a move for Callejon, but his agent Manuel Garcia Quilon hinted that both parties would be open to a new Napoli deal, despite no agreement being in place yet.
"[Napoli owner Aurelio] De Laurentiis has always wanted to renew his contract. We are grateful for the interest [he] has shown towards Jose and for how [he] has behaved with him, with his family and with me," Quilon told ABC Seville.
"At this time there is no agreement, the two positions are very respectable and there has never been a discussion of any kind between the parties.
"There is mutual affection, we have lived together for many years and these situations are part of football. We'll see."
Callejon joined Napoli from Real Madrid in 2013 and is fifth on their list of all-time appearance-makers with 336. body check tags ::