President Reagan formally notified Congress yesterday that he wants to begin negotiating an agreement with Canada that could erase all barriers to trade between the United States and its northern neighbor.

The two countries already form the world's largest trading bloc, with $120 billion in commerce passing between them last year. Reagan told Congress, moreover, that Canada is the United States' largest and fastest growing export market, accounting for more than $1 of every $5 in U.S. overseas sales.

Congress is seen as unlikely to block the talks, which are expected to start in late spring or early summer next year. Some lawmakers, however, are concerned about specific trade frictions, especially what they consider as Canada's subsidies of softwood lumber that is flooding American markets and hurting U.S. producers.

Under U.S. trade law, Congress has 60 legislative days to block the talks, but does not have to take affirmative action to approve them. Hearings by the House Ways and Means and the Senate Finance committees are expected after Congress returns from its year-end recess.

Reagan telephoned Canadian Prime Minister Brian Mulroney late yesterday afternoon to report he had started the process of getting legislative approval.

"I am aware that some members are concerned about pending trade disputes with Canada and have suggested that negotiations be delayed until these matters are resolved," Reagan wrote Sen. Bob Packwood (R-Ore.) and Rep. Dan Rostenkowski (D-Ill), the committee chairmen.

"I firmly believe that we should not delay. . . . The initiation of new bilateral trade negotiations may significantly enhance our efforts to eliminate current trade frictions with Canada, and in any event I assure you and the other members of your committee that the administration will do everything possible to resolve such disputes in a reasonable and timely manner."

Nonetheless, Sen. Max Baucus (D-Mont.) pledged to "do everything I can" to block the trade talks unless the timber issue is solved. "I am hopeful that Canada will show it is committed to fair trade and will act quickly to end its unfair timber subsidies," Baucus said.

U.S. Trade Representative Clayton Yeutter has promised Packwood, whose state of Oregon is a major U.S. lumber producer, that he would start separate negotiations shortly with Canada on the lumber issue.

At their Quebec summit last March, Reagan and Mulroney gave "the highest priority" to talks that would "reduce and eliminate existing barriers to trade" between the United States and Canada. After testing opinion, Mulroney told the Canadian parliament in September that he would seek trade liberalization talks with the United States.

The move was welcomed by the Reagan administration, which asserts a free trade philosophy and already has concluded a free trade pact with Israel. Bilateral trade talks with Canada, furthermore, strengthens administration arguments that it will negotiate separate arrangements if it is blocked in its efforts to broaden the power of the General Agreement on Tariffs and Trade (GATT), the international organization that governs world trade.

Among U.S. objectives in the talks with Canada are elimination of barriers to trade in services industries, such as banking, and to American investments. It also wants to end provincial laws, such as Ontario's liquor regulations, that are seen as barriers to U.S. products.

Canada, on the other hand, is anxious to gain legal relief from future U.S. trade barriers that could hurt its sales to this country, and would like to negotiate a separate U.S.-Canadian commission to settle trade disputes instead of having them go the usual route of having unfair trade cases decided by the U.S. International Trade Commission and Commerce Department.

Some opposition to liberalized trade has developed in Canada, with protected industries such as textiles, shoes and beer concerned they will be unable to compete with American manufacturers; farmers fearful they will lose subsidies, and nationalist groups worried about a loss of Canadian identity.