Los Che are keen to not see another young star leave and want to persuade the highly-rated Spain Under-21 international to sign an extension to his contract, which is due to expire in 2015.
Recent reports have claimed that United manager David Moyes is considering Bernat as an alternative summer transfer option to Southampton youngster Luke Shaw.
Napoli, meanwhile, are reported to have made an official enquiry for Bernat, but Rufete does not want to see the 21-year-old leave the Mestalla.
"Juan is a home-grown player from our academy and is a very important player for us," Rufete is quoted by calcionapoli24.it.
"We want him to stay with us for a long time, but we also know that there are many clubs that are interested in him because he is playing at such a good level.
"It is good that the team continues to produce such results and Bernat is certainly a player that interests Napoli and many other clubs, but our intention is to keep him."
Making Eduardo Vargas' loan move from Napoli to Valencia could be used in part of any offer from the Serie A side for Bernat, but Rufete is unsure.
The 24-year-old Chilean has been at the Mestalla since January and Los Che were tipped to try and keep him permanently in the summer.
"We cannot plan too much in the long term and have to think about the present more, which is to have a good end to the season," Rufete continued.
"At the end of the season we will see what happens, what the player says and what Napoli think.
"Now we are not thinking about what we are going to do with Vargas nor with any other player because we are focusing on doing well in Europe."