Former Texas governor John B. Connally said yesterday he will let the Republican convention delegates choose his running mate if he wins the GOP presidential nomination next year.

Connally, who declared his candidacy Wednesday, told reporters he had long disagreed with the notion that the presidential nominee should have "the exclusive right" to pick the vice presidential candidate.

His plan, he said, is to "name perhaps three people, any of whom would be completely satisfactory to me, 30 to 60 days before the convention, and let the convention make the choice."

Connally also hinted that he would break precedent in another way by remaining active in his Houston law firm and declining to make a personal financial disclosure before the convention.

Asked when he would sever his ties with his firm, he shot back, "When the members of Congress who are also seeking the nomination) resign from their positions... maybe a year from now -- maybe never."

As for disclousure, C onnally said, "I suppose candidates ought to look at the requirements for [people in] federal office... but I'm not sure any reports ought to be required until you become a nominee."

In his meeting with reporters, Connally defended his suggestion that the Constitution be amended to give a president a single, six-year term. He said relieving the chief executive of the burden and hope of reelection would encourage "a little more longrange consideration of fundamental problems."

He also said it would break the pattern of recent presidents "taking their campaign organization into office with them," and in that way, allow more competent staffing of the White House and key agencies.

While not ruling out a second-term bid for himself if elected for a fouryear term, Connally said he had told his newly hired political aides "they will not necessarily follow me to the White House."

Connally tangled with reporters on the question of whether he was being inconsistent in advocating a one-year, 5 percent, across-the-board cut in the federal budget and warning about the Soviet Union gaining a military advantage on the United States.

The onetime Navy secretary said the anti-inflation campaign justified a temporary reduction in defense spending. But he also said that, given the budget deficit, he applauded President Carter's decision to increase defense spending more than domestic programs.