Two sources spoke on condition of anonymity because a formal statement has not been released.
Friday is the deadline for Arkansas Attorney General Dustin McDaniel to file an appeal in the case.
A spokesperson for McDaniel said an announcement would come Friday, but wouldn't elaborate further.
State senator Jason Rapert, R-Conway, has called a press conference for Friday morning to discuss "developments in the litigation of Act 301 of 2013," according to an e-mail.
Act 301, also called the Human Heartbeat Protection Act, made Arkansas' abortion laws among the most restrictive in the nation.
A federal judge prevented the 12-week abortion requirement from taking effect in May 2013 and then permanently ruled that portion of the act unconstitutional last month.
However, the ruling preserved the "informed consent" portion of the statute, requiring women seeking to terminate a pregnancy to have an abdominal ultrasound before undergoing an abortion.
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