Smith and league commission chairman John Grant confirmed the amount of players under investigation at a media conference in Sydney on Wednesday.
The league heavyweights were adamant however that no players under investigation will be stood down from playing during the probing inquiry.
It was also announced that the investigation was to be conducted by ASADA for possible drug and substances use and not by Australian Crime Commission authorities.
Smith advised that all players under investigation would receive written notices to cooperate with ASAD officials.
Notices would be issued over the next 48 hours ahead another full set of league fixtures at the weekend.
"We don't know the extent of the outcome of these interviews and nor does ASADA," Smith said.
Smith revealed that up to 10 former players could be interviewed by ASAD officials also.
"It's 31 current players and a number of past players to form part of the investigation as well," he said.
"The former players are part of the anti-doping discussions.
"There is no mechanism if they are outside of the game for us to issue notices.
"There is no hint what-so-ever in anything to do with the ACC report.
"What we are talking about is 31 players that we have a relationship with.
"That will start early next week.
"Notices are being prepared as we speak and they will go out and it will take four to six weeks to get to the end of it."
The league boss said interviews would commence early next week.
Grant oulined a process the investigation will follow.
He expect ASADA investigators to complete interviews before any charges are laid.
If charges are laid they will be heard by an NRL tribunal with full legal representation for charged players to fight any allegations.
Grant reiterated that players will remain "innocent until proven guilty" and have a right of appeal if ASAD forces any playing bans.
Athletes found guilty of using performance enhancing drugs can be banned for two years.
Early confessions of guilt in breaching anti-doping regulations as well as cooperation with ASADA investigations can minimise a player's ban to just six months.