The White House said yesterday that it is looking into the circumstances surrounding gifts and bargain offers of stock in a small high-technology company that could benefit from President Reagan's effort to develop a futuristic anti-ballistic missile system.

Stock in Helionetics of Irvine, Calif., was given to physicist Edward Teller, who serves on the White House Science Council and has discussed lasers and related matters with presidential aides and with Reagan, The New York Times reported yesterday.

Stock also was offered at a bargain price to public relations executive Robert K. Gray and former treasury secretary William E. Simon, The Times said. Gray has ties to some White House aides, and Simon serves as an unofficial adviser to the president.

The gifts and offers were made by Bernard B. Katz, the principal shareholder in Helionetics, in what he described as an effort to attract prominent people to the firm's board of directors and as advisers.

The firm is one of many that could benefit from the president's March 23 "Star Wars" proposal to search for high-technology systems, possibly using lasers and particle beams, that would provide a defense against incoming Soviet missiles.

In the week before the speech, Helionetics stock rose by 30 percent, from $13.50 a share to $17.50, The Times reported. Teller was given 40,000 shares of Helionetics stock when he became a director in 1980, and his current holdings are valued at more than $800,000, the newspaper added.

George A. Keyworth II, science adviser to the president, said yesterday that Teller was not involved in preparations for the March 23 speech.

However, Teller did meet with Reagan last Sept. 14, the White House confirmed yesterday. Also present were Vice President Bush, Keyworth, presidential counselor Edwin Meese III and chief of staff James A. Baker III.

According to Keyworth, Teller wanted to explain to the president his interpretation of the nuclear freeze movement but also mentioned "the potential that he felt existed" from a laser system that would be powered by a nuclear explosion.

Keyworth said this "specific technology" was discussed but no mention was made of the later speech. In his address, Reagan did not specify a preference for any particular high-technology missile defense system.

Teller was named by Keyworth in early 1982 to the White House Science Council, an advisory group that reports to Keyworth and meets periodically. Teller is not required to file the regular financial disclosure reports provided by other government officials. Keyworth said he did not learn until yesterday of Teller's interest in Helionetics. However, he said Teller had informed his office of his stake in the company, though he did not know when.

While on the science panel, Teller has discussed with Keyworth "a host of new technologies" that would be useful from a national security standpoint, Keyworth said yesterday. Some discussions followed the Sept. 14 meeting with Reagan, but Keyworth said "none of Dr. Teller's views or inputs were transmitted to the president."

White House spokesman Larry Speakes said yesterday that presidential counsel Fred F. Fielding would look into the stock gifts. CAPTION: Picture, EDWARD TELLER . . . holdings worth more than $800,000