But the 25-year-old had to wait until this June to qualify for his adopted country and was immediately picked by head coach Andy Robinson for the summer tour.
Having scored two tries on his debut against Fiji and started this season with four tries for his club, Visser is showing no signs of slowing down either.
And Hastings, who captained the British and Irish Lions, believes that with a good RBS 6 Nations showing next year, Visser could make the 2013 tour to Australia.
"He could be a Lion but there is a step up from playing RaboDirect to international rugby," Hastings told the Scotsman.
"He has to go looking for the ball and be a dummy runner on a lot of moves. It is how he weighs up chances to continue his good form that will count.
"He knows there are still weaknesses within his game.
"What I like is the fact he is a Dutchman but one who is proud to play for Scotland."