Proving once again that Wall Street loves a good rumor -- even a tardy one -- more than 4 million shares of MCI stock changed hands Thursday after news reports of "serious talking" between MCI and IBM.

The reports were based on a story in the Silicon Valley Tech News published on Dec. 19 with the headline, "IBM Buys Rolm -- Is MCI Next?"

IBM and MCI officials vigorously denied they were involved in any discussions.

An IBM spokesman said, "There is nothing to it. We haven't bought MCI -- we haven't even thought about it."

The wave of trading raised the price of MCI stock Thursday by 7/8 to 8 3/4 but it retreated yesterday 1/4 point to close at 8 1/2. Yesterday's volume was 1,340,000 shares.

MCI, with 236.8 million shares outstanding, regularly is the most active stock traded over-the-counter by the National Association of Securities Dealers. On its record day in 1983, MCI traded 16.5 million shares.

The MCI-IBM reports were heard in the Washington area on Channel 50 via the Financial News Network, based in Santa Monica, Calif.

The information apparently was first aired on KCBS, San Francisco, by reporter Don Wiegandt, who said his report included denials from MCI officials.

Wiegandt said he had been told about the story by Frank Burkhard, editor and publisher of the Silicon Valley Tech News, which has a circulation of 55,000 and is published in Los Altos, Calif. Wiegandt said he had not been told about the story until some days after it appeared.

Reporter Brian Jeffrey, who wrote the story for the Silicon Valley paper, said he had two sources for his information that discussions had taken place between IBM and MCI officials and that he stood by his story.

In one passage, the story said, "IBM appears to be doing some serious talking with none other than MCI Corp."

But, said Burkhard, the information about discussions did not get any more definitive than that.

Burkhard said he has been told, since the story appeared, that MCI chairman William C. McGowan had been at IBM headquarters in Armonk, N.Y., but Burkhard said he had not confirmed the report.

MCI spokesman Gary Tobin said earlier that MCI has offices in that area of New York State and that MCI officials sometimes fly in and out of nearby Westchester County airport. Tobin suggested that someone might have seen McGowan and concluded he was there to talk with IBM. Otherwise, Tobin said, he could think of no reason for the reports.

IBM already owns part of another long-distance company, Satellite Business Systems. Analysts in the telecommunications field have suggested that IBM might use that route to go into the long-distance business.