1ppm means 1part/million (exp: 1mg/1000000mg) i.e. (1mg/kg).
But if you want to change the mass into volume i.e. tke kilograme to liter this is only with a liquide which its specific gravity is equal to 1 kg/liter ; here this liquid is distillate water at 1 atm and 4°C. so 1ppm is mg/liter of water at 4°C and 1 atm of pressure.
I am not disagreeing with Sellami but it is pretty routine to say that a liter of water weighs a kilogram somewhere near standard temperature and pressure which is 1 atm and 20 C or room temperature.