Sources say authorities have written a draft criminal complaint that could be filed as early as Thursday. Kopp, 44, remains at large, his whereabouts unknown.
Slepian was shot to death last October by a sniper with a high-powered rifle as he sat in the kitchen of his Buffalo, N.Y. area home. He was the fifth abortion provider shot by a sniper in upstate New York and Canada since 1994. He was the first of them to die.
The U.S. Attorney for western New York has scheduled a news conference for Thursday.
Kopp has been named a material witness in the Oct. 23, 1998 shooting death of Slepian, 52, who was one of only three doctors who performed abortions in the Buffalo area.
Law enforcement sources have previously told CNN that circumstantial evidence suggests Kopp may have been involved in or had some knowledge about the crime.
He has never been named as a suspect in the case.
Long-time abortion foe
Kopp has been missing since shortly after Slepian's killing and soon after federal officials issued the material witness warrant for his arrest. The search for him has led investigators on a hunt from Canada to Mexico with no luck.
One witness reported seeing Kopp's car parked near Slepian's home at dawn 10 days before the shooting. Investigators found his 1987 black Chevrolet Cavalier parked at Newark International Airport in December and said it had been there for a while.
Police found hair samples and bullets near the sniper's position the day after the shooting and a month ago located the rifle and some clothing outside the victim's home.
Kopp is a long-time anti-abortion protester who has taken part in demonstrations across the country for years. He was arrested in 1990 in West Virginia after participating in an anti-abortion protest and in Burlington, Vermont, where he locked himself to the axle of a car.
In another protest, Kopp used specially made locks of iron and concrete to link himself to other protesters. Kopp used the same technique during protests at a Long Island women's clinic in 1991.