Democratic Gov. Rudy Perpich said today he plans to meet next Tuesday in Florida with Muriel Humphrey to ask her if she'll succeed her late husband, Hubert H. Humphrey, in the Senate.

The St. Paul Pioneer Press said today that sources close to both were sure Perpich had already offered to appoint Mrs. Humphrey and she was "99 per cent certain" to accept an interin appointment as a caretaker senator until the November general election. In Minneapolis, one of Humphrey's oldest political friends said: "That's on the right track."

Mrs. Humphrey and her daughter and son-in-law - Mr. and Mrs. C Bruce Solomonson of Minneapolis - are scheduled to leave Saturday from Weverly, where Humphrey died last Friday, for vacation. They are scheduled to fly first to Florida and then, on Wednesday, to a resort in the Virgin Islands, Caneel Bay Plantation.

Caneel Bay was a favorite get away place for the Humphreys when the senator was alive. If necessary for purposes of his negotiations, Perpich will continue to the Virgin Islands, his press spokesman, Bob Aronson, said today.

Although Mrs. Humphrey's Florida destination wasn't announced, sources familiar with her plans here said that she would stay with friends in Fort Lauderdale. She plans to return to Minnesota Feb. 8 by way of Washington.

In another development, Rep. Don Fraser (D-Minn.), who is expected to announce officially next week that he will seek election in November to the Humphrey seat, urged Perpich to appoint Mrs. Humphrey.

Under present law, the governor appoints an interim senator, with an election to complete the remaining four years of the Humphrey term in November. Perpich has indicated clearly that he prefers a "caretaker" successor without embitions to seek the seat by election along with the rest of the ticket in November.