The number one goalkeeper has been attracting attention with some impressive displays in the past 18 months.
There are even rumors of interest from Juventus, where he would be second choice if he signed.
He has a contract at Newcastle until 2022, with hopes of a renewal.
His agent Pavel Zika told Ruik in Czech Republic: "We can confirm that Martin belongs to the Juventus scout department's list of long-term players.
"However, we must mention that it is not only monitored by Pavel Nedved's Juventus, but there are also Premier League clubs. Our personal tip with my brother is that Martin stays in England.
"Our effort, but also Newcastle's endeavour, is to negotiate a new contract at the end of this season, as Martin came to Newcastle as a virtually unknown Czech league player, but quickly became a major player of the entire team and already has an excellent reputation throughout the English league.
"So we are gradually starting to negotiate an improved contract, but of course, on the other hand, we record interest from a number of other clubs in the English league. Martin Dúbravka is in agreement that our goal is to prove as much as possible in England."