If confirmed, the move would remove a threat to Sharon's continuing in office.
The case concerns a failed property deal. Businessman David Appel has been charged with bribing Sharon and one of his sons over a project to turn a Greek island into a tourism centre.
But in order to convict Sharon of receiving a bribe, criminal intent would have to be proved on his part.
Channel Two and Channel 10 opened their newscasts on Monday evening with a report that Attorney General Meni Mazuz concluded that there was not enough evidence to indict Sharon, and he would announce by 15 June that the case was closed.
An indictment would probably force Sharon from office, at least temporarily.
Responding to the reports, Justice Ministry spokesman Jacob Galanti said: "Discussions on the case are continuing. No decision has been made and when we make a decision, we will announce it."
Sharon also faces the possibility of charges in another case - a questionable loan from a South African businessman to cover illegal campaign contributions in a 1999 election race.