Senate Majority Leader Howard H. Baker Jr. fueled speculation today that he will retire at the end of his present term in 1984, but denied that he planned to run for the GOP presidential nomination next year.

"Would I like to run for president someday?

"Sure I'd like to run for president," he said, fielding questions at a news conference that virtually upstaged the inauguration of Gov. Lamar Alexander, a former aide and Baker protege.

"But if you're asking me if I decide not to run for reelection for the Senate, does that signal a determination to run for president, no it does not," he said.

In his first public appearance after a Florida Everglades vacation, Baker said he expects President Reagan to run for reelection and plans to support him. "I think he will run. I think he should run. And I will support him," Baker said.

"If President Reagan runs and is elected to a second term, then those of us who are interested in the presidency would have ample time to figure out what we do next," he said. Baker expects Reagan to announce "with clarity" a decision to run again "sometime this year."

He brushed off accounts that he was leaning against running for another Senate term to send the White House a message that key Republicans view Reagan as vulnerable. "I wasn't trying to send the president a message, but it was only microseconds" after the story broke that the White House phoned to ask "what that meant," Baker said.

"The president knows I support him," he said.