Martina, 27, was released by Southampton earlier this month after two rather unsuccessful campaigns in Hampshire but could be plying his trade in the Premier League next season, with Koeman keen to bolster his full-back options as Seamus Coleman recovers from a broken leg.
When asked about Everton's reported interest, Martina, the only Curaçaoan to ever play in England's top-flight, did not hide his desire to move to Merseyside.
"Yes, I've read (the reports linking him to Everton), but I don't know anything about it now," Martina told FoxSportsNL. "Do I want it? Yes, Everton is a very big club. Who doesn't want that?"
Martina made 18 appearances for Southampton in all competitions last season, with the last of those coming in January.
Despite being seemingly frozen out by Claude Puel, whose spell in charge at The St Mary's Stadium is set to come to an end this summer, Koeman remains a fan of the former Twente defender, who can also operate as a centre-half.
With Everton's season set to start in July due to their Europa League commitments, Koeman is keen to conduct his transfer business swiftly.
The Toffees are in talks to sign Ajax midfielder Davy Klaassen, who could cost around £26m, while Malaga forward Sandro flew into Liverpool on the weekend to meet Everton's director of football Steve Walsh and discuss a potential deal, according to The Guardian.
Along with Sandro and Klaassen, the Toffees are interested in Burnley defender Michael Keane, Sunderland goalkeeper Jordan Pickford and Swansea City playmaker Gylfi Sigurdsson, while the futures of star attackers Ross Barkley and Romelu Lukaku are far from certain, with the latter recently suggesting that remaining at Goodison Park is 'not an option'.