The Gunners are set to run the rule over the 20-year-old, who was previously offered a trial by Brighton & Hove Albion.
Smith left NEC Nijmegen at the end of the campaign and was previously offered a chance to impress Championship promotion hopefuls Brighton & Hove Albion earlier this year.
Arsene Wenger's side currently have an abundance of goalkeepers on their books, though both David Ospina and Wojciech Szczesny - who spent last season on loan to AS Roma - have been linked with moves away from the Emirates Stadium this summer.
Is Szczesny on his way out?
And Smit told Dutch outlet De Gelderlander, as quoted by the Daily Mail: "This opportunity I have to seize."
The 20-year-old, who left Vitesse Arnhem for Nijmegen a year ago, is yet to make a single appearance at senior level.
Arsenal have made two signings already this summer, with Swiss midfielder Granit Xhaka arriving from Borussia Monchengladbach and Japanese striker Takuma Asano following from Sanfreece Hiroshima, subject to a work permit being granted.
Xhaka was Arsenal's first summer signing
As well as Ospina, Szczesny and Petr Cech - a £10 million signing from Chelsea a year ago - Gunners boss Arsene Wenger has Emiliano Martinez, Deyan Iliev, Matt Macey and Ryan Huddart to call upon between the sticks.
Ospina is another high-profile keeper on Arsenal's books