President Reagan has invited the new Soviet leader, Mikhail Gorbachev, to a summit meeting at a "mutually convenient time," administration sources said yesterday.

The invitation is included in a "personal message" being carried by Vice President Bush, who is leading the U.S. delegation to the funeral today of Soviet President Konstantin Chernenko.

Reagan overruled his foreign policy advisers this week and decided not to go to the funeral, which most other major Western leaders are attending. Several of his top advisers had urged Reagan to make the trip as a gesture of good will toward the Soviets at a critical time in superpower relations.

While rejecting this advice, saying that a trip to Moscow would not be worth the time and effort it would require, Reagan opted for another gesture toward Gorbachev, an invitation for a summit meeting at an unspecified future date and location, officials said.

Bush is expected to deliver the invitation to Gorbachev today. Reagan told reporters yesterday that Bush would discuss a summit meeting in Moscow "if he has the opportunity."

On Monday, the president said he was "more than ready" for a meeting with Gorbachev once he is in place and can "establish his regime."

For most of Reagan's first term, when he was taking a hard line toward the Soviets, he attached stiff requirements to any consideration of a summit meeting, including that it be well-prepared in advance, have a reasonable chance of success, and, at one point, that the Soviets improve their behavior around the world.

Reagan eased some of those conditions last summer, and yesterday White House officials suggested that U.S.-Soviet relations had improved significantly and thus increased the prospects for a summit.

In a carefully worded statement, White House spokesman Larry Speakes said, "If it is possible to arrange such a meeting, with full and careful preparations, we believe it would make a constructive contribution to the development of our relations with the Soviet Union."

Speakes also told reporters that Reagan would "assess the pros and cons" of a possible summit if "the opportunity presents itself." He said the "atmospherics" of U.S.-Soviet relations had improved over the last year or so, with the resumption of negotiations on nuclear weapons, and the beginning of new leadership in Moscow.

Reagan is the first president since Herbert Hoover not to meet with the leader of the Soviet Union during his presidency. He did not meet with any member of the Soviet leadership in his first term until last September's session with Foreign Minister Andrei Gromyko.

Yesterday, an informed White House official said relations have improved since the last Soviet leadership change when Chernenko took over from Yuri Andropov.

Gorbachev is "healthy enough to meet with President Reagan. He has moved quickly and is likely to be in power" for some time, the official said.

Speakes said "we welcome the tone" of Gorbachev's first speech, noting his call for an end to the arms race and his statement that "the Soviets do not strive to ac- quire unilateral advantages over the United States or over NATO countries . . . . "

The White House official, who asked not to be identified, said British Prime Minister Margaret Thatcher had recently described to Reagan her meeting with Gorbachev, and he is "someone we want to meet with."

"Take it back a year," the official said. When Chernenko took over, he went on, the arms negotiations were stalled and there were still reverberations from the Soviet downing of Korean Air Lines Flight 007. "Relations were at a nadir," the official said.

In contrast, the official said, today the arms negotiations are resuming, Reagan has met with two Politboro members -- Gromyko and just recently, Vladimir Shcherbitsky -- and Reagan was reelected.

In the last year, Reagan has also softened the harsh "evil empire" language of his first three years in office.

Officials said they could not put a timetable on a possible summit meeting, but they said Gorbachev would need time to take the reins of power in Moscow. "It does make sense to let him settle in first," the White House official said.

"If the opportunity presents itself, we will weigh all of the factors, pro and con, for the prospects of having a good meeting with the Soviet Union, and at that time we will make our decision," Speakes said. One measure of possible success, he said, is whether it would be "beneficial to the cause of world peace to participate in a meeting with the Soviet leaders."