Bestselling author Tom Clancy found out yesterday that he has a fan in the White House: the commander in chief. In a five- to 10-minute chat in the Oval Office, President Reagan praised Clancy's book, "The Hunt for Red October," and told him that he found it "non-put-downable."

In a short discussion of the mechanics of writing an espionage thriller, Reagan told Clancy he was reminded of a story. The president said he had just received a letter from a sailor serving on a U.S. submarine who wrote that the United States may not have the biggest navy in the world but it sure had the best one, Reagan said.

The president asked Clancy if he was writing another book and the Calvert County, Maryland, insurance man said he was and that it was on World War III. "Who wins?" Reagan asked. Replied Clancy, "The good guys."

Clancy and his wife Wanda, escorted by Deputy Chief of Staff Michael K. Deaver and Reagan intimate Nancy Reynolds, went to lunch in the Roosevelt Room with about 25 other guests, including Navy Secretary John Lehman Jr., Energy Secretary John Herrington, Sen. Mark Hatfield (R-Ore.) and retired Air Force general Brent Scowcroft.

Reynolds said she had just returned from Vienna where she represented the United States at an international women's meeting. At the meeting, she said, she gave a wrapped copy of "Red October" to her Soviet counterpart, a man, saying that President Reagan had liked the book and Reynolds was certain the Soviet would find it interesting reading.