During the summer window, the Magpies allowed the Slovakian to move to Manchester United on a season-long loan deal.
While the 33-year-old had been expected to remain at Old Trafford.
According to the Daily Mail, the Foxes are now interested in negotiating a deal for Dubravka over the coming days.
Despite keeping six clean sheets in the Premier League this season, doubts remain over whether Danny Ward will remain the first choice at the King Power Stadium in the long term.
With Dubravka still having a contract at St James’ Park until 2025, Newcastle may insist on receiving a notable fee should they agreed to sell a player who racked up 130 appearances for the Tyneside outfit.