The News-Times of Danbury reports that Neil Heslin of Shelton has until July 9 to accept the plea deal.
Heslin's case involves motor vehicle charges and allegations he issued bad checks to purchase building materials for his construction company.
Judge Frank Iannotti on Wednesday noted that Heslin has made restitution. Under the deal, Heslin would plead guilty only to driving with a suspended license.
Heslin and his attorney, public defender Bruce Weiant, declined comment.
Heslin has become an outspoken advocate for gun control since his son, Jesse Lewis, and 25 others were killed in Newtown on Dec. 14.