There have been suggestions that Arsenal new boy Alexis Sanchez has urged the Gunners to sign international teammate Vargas, but no action seems to have been taken yet.
Vargas is expected to leave Napoli before the transfer window closes as he is seen as surplus to requirements at the Stadio San Paolo.
The 24-year-old has struggled to feel at home in Italy and has spent the last two seasons out on loan to Gremio and Valencia.
After a decent World Cup campaign, Vargas is likely to have several teams interested in luring him away from his current employer, but Arsenal may not be one of them.
Reports stating that Vargas could be involved in a swap deal with Arsenal's Costa Rica international Joel Campbell seem to be nothing more than gossip.
"I haven't been contacted by anyone."
A more likely move for Vargas may be to return permanently to Spanish side Valencia where he made 17 appearances last season.
"Is he going to Valencia? The truth is that at the moment there are no official offers and I have only heard this link through rumours in the press."
Vargas has a year left on his contract and is widely valued at £10 million, but Arsenal manager Arsene Wenger has ruled out any further attacking signings and may stick to his word.