Pete Rose, reportedly seeking a salary of $750,000 as the Cincinnati Reds' player-manager for next season, is close to signing a contract, club officials said yesterday.

Rose, who earned a base salary of $225,000 and $120,000 in an attendance bonus this past season, met Monday with Reds General Manager Bill Bergesch to begin working out 1986 contract terms. "This was our first substantive discussion," said Bergesch. "Money and years, those are things we're discussing. We're rapidly working this out. I don't anticipate any problems . . . "

The Reds, after finishing next to last in the National League's West Division in 1984, finished second in 1985, Rose's first full season as player-manager. Reds President Marge Schott said Rose deserves to be rewarded.

"We're going to take care of Pete, there's no doubt about that," she said. "We have to have him. I want to show him my appreciation, but he has to do the same thing for me."

If Rose gets the $750,000 he reportedly is seeking, he would become baseball's highest-paid manager. Earl Weaver of Baltimore is believed to be the current highest-paid manager. Although the Orioles refuse to discuss the terms of his contract, Weaver recently signed a one-year deal for 1986 worth reportedly $600,000 . . .

The Chicago White Sox signed Manager Tony LaRussa to a one-year contract following a meeting between LaRussa and new club operations director Ken Harrelson. LaRussa, who has managed the White Sox since August 1979, said Harrelson and the rest of the front office convinced him to stay.

"Yes, I had some doubts and I had to consider the possibilities," LaRussa said . . .

Former Washington Senators pitcher Dick Bosman, an assistant baseball coach at Georgetown University for the past two years, will become the Chicago White Sox' AAA pitching coach.