New CEO Ben McDevitt said the agency was working towards issuing the notices with "urgency" but it did not want to "sacrifice certainty for speed".
He also said he had held "a couple of conversations" with incoming AFL CEO Gillon McLachlan, who officially takes over from Andrew Demetriou this week, and had met NRL CEO David Smith once in the past month.
Essendon and NRL club Cronulla have been under ASADA investigation for more than a year.
"We do have reputations hanging in the balance and potentially people's careers could be damaged," McDevitt told a Senate hearing on Tuesday.
"We want to do it quickly but we want to get it right ... we are talking weeks here, not months."
McDevitt took over from Aurora Andruska in the past month.
He rejected any suggestion the inquiry process had been slow nearly a year and a half after "the blackest day in sport" on February 7, 2013.
On that day, the Federal Government released the Australian Crime Commission's findings over the widespread use of drugs in sport.
"There are some examples of cases offshore ... involving one athlete in one sporting code, and you're talking three years plus," McDevitt said.
"So when you're talking two sports, multiple athletes, perhaps we might see the 17 months a little more in context."
Fairfax Media said McDevitt told the Senate hearing he had read a report on the AFL and NRL cases completed by retired federal court judge Garry Downes that was handed to ASADA on April 28.
He said he was yet to digest "the enormous amount of material" gathered in the investigation.
This included more than 300 interviews running as long as nine hours each, and 150,000 documents, some of which were up to 200 pages long.
On Monday, Demetriou called for ASADA to finalise its investigation into Essendon's 2012 supplements program, while acknowledging his sympathy for the Bombers during the lengthy process.
The club remains none the wiser about when - or if – players will be issued with show-cause or infraction notices.
Demetriou said the lack of communication from ASADA was disappointing.
"It's very frustrating and I've got enormous sympathy for the club and the players," he told radio station 3AW.
"We do need to have some finality to this issue and it has to be stressful on the players, in particular.
"It doesn't matter which way you cook it, the uncertainty cannot be a good thing."
