Industry sources told the South Korean news service Yonhap that the refurbished device would be known as the Galaxy Note FE and cost less than 700,000 won (about US$616).
It is expected to go on sale on 7 July.
The Note7 was initially released in August last year. A month later, reports of exploding devices and resultant fires started to pour in.
An investigation into the incidents revealed the Note7 issues were caused first by a battery from one supplier (Samsung SDI) that was too large for its casing and a manufacturing flaw in the line of batteries (made by Amperex, a second supplier) when production was ramped up to replace the first set of phones that blew up.
Yonhap said the refurbished devices would have a smaller battery capacity than the originals, and also include latest software updates.
It said: "Samsung has been planning to release the Note FE amid criticism that to totally discard all the existing phones it bought back from consumers or did not sell could adversely impact the environment."