The Amsterdam giants failed to lure the attacker away from Heerenveen in the January transfer window, but the winger is hopeful that the move will materialise this summer
The reigning Eredivisie champions already made an offer for the Heerenveen winger in January, but were unable to complete the deal before the transfer window slammed shut.
Ajax are still interested in signing Narsingh and the 21-year-old is keen to return to his boyhood club this summer.
"I do not want to move abroad yet. So the logical next step in my career is a big club in Netherlands," he said to NUsport.
"Ajax meet that criteria. I would not have to think twice if I got the chance to move there. There was not enough time to complete the move [in January]. It might happen after this season though."
Narsingh is a product of the Ajax youth academy, but never made the first team in Amsterdam.
"I've read that my transfer fee is €6 million now. And to think Ajax could have had me for free."
The youngster has a contract with Heerenveen that runs until the summer of 2013.