Mayor Jane Byrne said today that she will endorse Sen. Edward M. Kennedy (D-Mass.) for president because she believes President Carter cannot win reelection.

The Byrne endorsement will virtually assure Kennedy of the 49 votes of the Democratic organization delegates in the Chicago congressional districts. tHowever, Carter will still battle Kennedy for the other 130 suburban and downstate delegates to be elected in the March 18 Illinois primary.

More broadly, her support may trigger a run of endorsements from other local Democratic leaders for Kennedy, who is slated to announce his candidacy before Thanksgiving. Carter has sought to bolster his position with endorsements from the mayors of New York, Lost Angeles, Detroit and other big cities, as well as 20 governors, but Byrne's action may be the start of a counterwave of Kennedy endorsements.

Byrne told reporters she would not make a formal announcement before Tuesday because she did not want to detract from the unveiling of Kennedy's exploratory campaign committee Monday.

"I don't want to detract from his press," Byrne told reporters who cornered her at a hotel meeting to ask about rumors she was backing Kennedy.

The mayor denied she was changing her mind about Carter, although on two recent occasions she said she would back him for reelection. "I told the president I could support him, until I thought he could not win," Byrne said.

Robert Torricelli, the Illinois Carter campaign director, said Carter still intended to push hard in Illinois. "We hope that for Sen. Kennedy's sake the endorsement he has received from the mayor is more meaningful than the one that President Carter enjoyed last week,' Torricelli said.

Torricelli was referring to the support Byrne gave Carter on Oct. 15 when the president attended a fundraising dinner here for the mayor.At the dinner, Byrne said that while she couldn't presume to speak for the Cook County Democratic Party, if the election were held that night she would vote for Carter.

"The election wasn't that night," Byrne said today. Byrne said she has since taken a nonscientific telephone poll that showed her Carter could not win in Illinois, and has discussed the findings with county party chairman George W. Dunne. She said Dunne concurred in her decision to endorse Kennedy.

Asked if she might change her mind about Kennedy, Byrne said that the coming endorsement "will go clearn through November and until a Kennedy returns to the White House." Byrne got her start in politices in 1960 working in the campaign of John F. Kennedy.

Disclosing that she has talked with Sen. Kennedy about 10 times in recent weeks, Byrne said, "I think he will sweep the convention."

Many of Chicago's Democratic ward committeemen have been urging Dunne and Byrne to back Kennedy. The committeemen feared that Byrne's announced intention to field an uncommitted slate of delegates to the national convention might fail because mavericks can run ledged on the ballot to Kennedy.

Byrne said her decision was also influenced by a number of pressing economic issues: rising interest rates; the increasing cost of living; the inability of many Chicagoans to sell their houses in the current real estate market.

She said Carter is "despearately trying, but I think the programs he's leading aren't working. I think the president is a very good man and a very honest man and that he has integrity."