The 20-year-old full-back has been in regular contact with boss Derek McInnes throughout the summer window, and a move up to Glasgow now looks likely, per Jacob Tanswell of The Athletic.
Rangers' obligation to buy Nedeljkovic would be based on appearances, and is worth an estimated £4 million.
The Serbian has been involved in Villa's pre-season under Unai Emery, but has been made available to leave, as they look to strengthen their full-back department and provide competition for Matty Cash.
It comes as Villa continue to chase West Ham's Aaron Wan-Bissaka, who has been high up the transfer list for Emery this summer.
But for McInnes and Rangers, they will hope the signing of Nedeljkovic can provide some much needed attacking prowess at full-back, as Dujon Sterling and Ross McCrorie are viewed as more defensive-minded players.
The Rangers boss has been keen to bolster his squad further, having won just once out of his five games in charge so far.