Adams, 39, succeeded John Sheridan at the helm on June 11, but has just 14 players contracted to the club.
“I had a meeting with the chairman yesterday to go over the budget and everything, so then we can go forward and try to get players in,” Adams told BBC Sport.
“I don’t see it being in the near term but we’re working on it.”
Argyle just missed out on promotion having been knocked out in the League Two play-offs last season.
The Pilgrims have agreed a new deal to keep reserve goalkeeper James Bittner, who will also become the goalkeeping coach following the departure of Rhys Wilmot.
Former Ross County manager Adams has also had talks with the out-of-contract 22-year-old Anthony O’Connor and 19-year-old Tyler Harvey, but deals have yet to be agreed.
Adams added: “We obviously have to add to the squad, and depending on the budget we’ve got, we’ve got to work to the constraints of that and be ready for August 8.
“We’ve assessed what we have in the squad, we’re assessing the players we’re going to take in and we’ll get to the point where we’ll obviously make signings.”