Jesse Jackson is expected to announce that Jerry Austin, an Ohio-based political consultant who managed the 1986 campaign of Ohio Gov. Richard F. Celeste (D), will be his campaign manager. Jackson spokesman Frank Watkins yesterday would say only that a news conference is scheduled for Friday to announce a national campaign chairman and other campaign officials.

But Jackson said this weekend that he has met with Austin, who had been in Iowa the week before, and that it is just a matter of working out details. Austin, vacationing in Bermuda, said yesterday, "We've had serious discussions and are in the final negotiations, but my name is not on the dotted line."

Meanwhile, on Saturday, Jackson was endorsed by the Alabama New South Coalition, one of the state's two powerful predominantly black political organizations. Birmingham Mayor Richard Arrington, who heads the ANSC, called Jackson's chance of winning the nomination "slim" but said that as a "team player" he would support Jackson. In 1984 Arrington endorsed Democrat Walter F. Mondale. One Alabama Democratic official said, "It remains to be seen if Arrington will go all out for Jesse as he did for Mondale."

The Alabama Democratic Conference, ANSC's rival, plans to make an endorsement in early December. It is expected that it, too, will endorse Jackson. In 1984, the ADC went with Mondale.