President-elect George Bush said Wednesday, if President Reagan vetoes a controversial ethics bill, he will send Congress his own strong measure next year.

"Let's wait and see what the president does," Bush, who supported the ethics bill during the 1988 presidential campaign, told reporters during a question-and-answer session after he named Brent Scowcroft his national security adviser."But if this bill is not signed, I will send up an ethics bill," he said. "I'm determined to fulfill that general posture that I've taken in terms of ethics in government." He said any ethics bill he submits "will be a strong one; it will be a fair one."

Asked about the bill now on Reagan's desk, co-sponsored by Sen. Strom Thurmond, R-S.C., Bush said, "There is some recognition that the Thurmond bill was a very good start" but that there were "some changes made in it that I guess nobody is really totally happy with."

The Washington Post reported Wednesday that Reagan had decided to veto the bill despite Bush's urging that Reagan sign the measure that would tighten restrictions on lobbying by former federal officials.

Many Reagan administration appointees about to leave government with the change of administrations could be adversely affected by the bill and some Cabinet members and top White House aides have lobbied Reagan to veto it, the Post reported.

Bush, who approved of the bill during the campaign, has privately recommended to Reagan that it be signed, the Post said, quoting sources.

The Post-Employment Restriction Act, popularly known as the "ethics" bill, would limit for one year government contacts by former federal officials and members of Congress and bring them under the same ethics restrictions that apply to high-level administration officials under the 1978 Ethics in Government Act. The measure overwhelmingly passed Oct. 21, the last day of the 100th Congress.

Reports surfaced over the weekend that Cabinet officials, led by Interior Secretary Donald Hodel and Transportation Secretary James Burnley, are urging Reagan to veto the bill, and the Post reported Wednesday that Attorney General Dick Thornburgh, Secretary of State George Shultz and Secretary of Defense Frank Carlucci also have weighed in against it.

While White House spokesman Marlin Fitzwater said Tuesday there is "no decision on the ethics bill," he added that Reagan will make his choice by Friday, the deadline for action.

On Tuesday, Bush met in Houston with incoming Mexican President Carlos Salinas de Gortari for a get-acquainted session. Both he and Salinas, who takes office Dec. 1, called the meeting a first step toward improved U.S.-Mexican relations.

Over a six-course lunch that included roasted pheasant and gilded chocolate truffles, Bush and Salinas discussed drugs, immigration, trade and Mexico's staggering $102 billion international debt, aides said.

"I am absolutely confident after this initial visit that we're both committed to improving a bilateral relationship," Bush said.

Salinas, using similarly upbeat diplomatic language, called the session "a positive, respectful, cordial dialogue which I am certain will do a great deal to improve the relations between Mexico and the United States."

The vice president, in remarks applied to both Mexico and Canada, pledged to "never neglect our own friends in this hemisphere."

In an address earlier to a meeting of Republican governors in Point Clear, Ala., Bush congratulated Canadian Prime Minister Brian Mul-roney for a "spectacular win."

Bush called Monday's election a ringing endorsement not only for the prime minister but also for the recently negotiated U.S.-Canadian free-trade pact.

Bush said that while he still hopes to meet with Massachusetts Gov. Michael Dukakis, he did not think such a meeting would take place this weekend.

The campaign between Bush and Dukakis was noted for its bitter tone, but Bush told supporters at an Election Night party that Dukaksi had graciously conceded defeat in "the best spirit" of American politics.