Mertens, 32, who is out of contract this summer, would cost at least £5m.
Aside from attracting interest from Chelsea, Inter Milan are also being linked with Mertens.
Chelsea manager Frank Lampard has become increasingly frustrated by lack of signings this month, particularly in an attacking area.
Young striker Tammy Abraham has been shouldering the scoring responsibilities so far this season.
And Mertens who can play in any position across the front three is being lined up to replace Olivier Giroud, who has been linked with a move away from Stamford Bridge.
Speaking about Mertens in December, agent Federico Pastorello said: “If I think about a good opportunity in the market, it would be Mertens from Napoli. He is out of contract (in the summer).
“He is an amazing player. I think he will be soon the best scorer in the history of the club. He has proven himself in the Champions League because he scored in that competition and the national team. I think a player like that, out of contract is an amazing opportunity, even maybe for January,” he said about Mertens.
“Every player really wants to play in the Premier League at least once. So I think he would be very happy to play in the Premier League. I know him very well tactically and technically and I think he can be a successful player for the Premier League.”
11 BUSINESS NUGGETS FROM SUPER EAGLES BRONZE MEDAL TRIUMPH. The content of this ebook will propel you above your competition. DOWNLOAD NOW!!!