Senate Minority Leader Robert Dole (R-Kan.) took a cautious approach yesterday to President Reagan's nomination of Judge Douglas H. Ginsburg to the Supreme Court as two inquiries were examining whether Ginsburg had a conflict of interest in actions he took as a Justice Department official on cable television issues while holding stock in a Canadian cable television firm.

In a remark reflecting the uncertainty of senators in both parties about Ginsburg, Dole said, "I want to hear about the cable thing myself" after attending a White House meeting at which Reagan expressed his full confidence in the nominee. Dole added that Ginsburg "has a short paper trail, so every little thing that comes up is magnified."

Asked whether his support of Ginsburg would be "automatic" because he leads the president's party in the Senate, Dole replied, "I'm almost automatic" but said he wants to know more about the cable television issue.

White House spokesman Marlin Fitzwater said the Office of Government Ethics is looking into Ginsburg's actions on the cable television matters while he was a senior Justice Department official. Ginsburg argued against regulations opposed by the cable television industry and supervised a major anti-trust investigation into the industry when he held almost $140,000 in stock in Rogers Cablesystems Inc., a Toronto-based cable television firm.

"We are confident that when they have reviewed all the facts, they will find no conflict," Fitzwater said. "We believe there is no conflict of interest or even the appearance of conflict of interest."

An American Bar Association panel is also examining Ginsburg's actions as part of its broader evaluation of his nomination to the Supreme Court, according to former Judge Harold H. Tyler Jr. of New York, chairman of the bar association's Standing Committee on Federal Judiciary Members.

Also yesterday, two lawyers who represent Rogers Cablesystems said the outcome of Ginsburg's work at the Justice Department on cable television matters could have had both positive and negative financial impact on the company. The question of whether the company was affected is important because Justice Department rules prohibit employes from participating "personally and substantially" in matters in which they have a "financial interest."

Wes Heppler, a Washington lawyer who represents Rogers, said comments filed before the Federal Communications Commission by Ginsburg in 1986 "had the potential for a direct impact" on the company. In the comments, the Justice Department argued against forcing cable companies to carry certain local channels.

Justice Department spokesman Terry Eastland, speaking for Ginsburg, said Ginsburg's name was typed on the document and he was informed of the position taken, "but he was not the signatory official."

Another lawyer, Warren G. Lavey of Chicago, who also represents Rogers, said Ginsburg's argument in a 1986 Supreme Court case that cable companies should enjoy First Amendment protections could have hurt Rogers.

Lavey said that in a 1986 stock offering, Rogers Cablesystems said that the position Ginsburg argued "may adversely affect the profitability of the company's systems."

Eastland said Ginsburg had decided that Rogers "would not be affected financially" by the decision, and so he proceeded to play a central role in the case.

Ginsburg may also face questions about whether he followed Justice Department rules when deciding whether to handle cable televison matters. The rules require that officials consult with their superiors when faced with a potential conflict of interest. Eastland confirmed that Ginsburg did not consult with his superior at the time, Deputy Attorney General Arnold I. Burns, but instead asked his subordinates whether he should remain involved in the Supreme Court case.

The rules also say that department officials should obtain a written waiver from the deputy attorney general when they are faced with possible conflicts of interest. Ginsburg did not seek such a waiver.

Also yesterday, Fitzwater charged that the American Civil Liberties Union is preparing to "gear up a political campaign" against Ginsburg and was thus seeking a delay in the hearings. Leslie Harris, ACLU legislative counsel, said the group has not decided to oppose Ginsburg and urged a 60-day delay to allow time for the Senate to "fully develop the record" regardless of who was chosen.

Other senators also indicated they are taking a cautious approach to the nomination. "I think people are laying back and waiting to see what this man really believes," said Sen. Dale Bumpers (D-Ark.). Added Sen. Arlen Specter (R-Pa.), a swing vote on the Judiciary Committee, "There's a consensus that all the information should be disclosed and put on the table as soon as possible."

Although the White House is pushing for early hearings, Judiciary Committee chairman Joseph R. Biden Jr. (D-Del.) indicated that hearings will not begin until after the bar association report is complete, which Biden said is "probably not possible before Thanksgiving." Biden said he is "amenable" to starting hearings in December. He said the committee will look into cable television matters as well as Ginsburg's views on various constitutional issues.

Staff writer Helen Dewar contributed to this report.