A 39-year-old Democrat from Silver City, Morales said in an interview Wednesday that he is interested in the job and likely will pursue it.
He said he believed that Democrats must emerge from their caucus next month united behind one candidate for the Senate presidency.
"We don't want to dilute our vote to put ourselves in jeopardy," he said.
Democrats will have a 25-17 advantage in the Senate next year. That means a bloc of at least 22 Democrats — without any say-so from Republicans — can choose the chamber's next president.
Morales says he has the skills, experience and temperament to become the Democrats' choice.
A former Grant County clerk and teacher, he holds a Ph.D in curriculum and instruction. Morales specializes in finance and education issues in the Senate, and is regarded by his colleagues as one of the chamber's best orators.
At least three other Democratic senators have said they would pursue the Senate presidency, but Morales said the field may thin to two by the time of the caucus.
Also saying they will run for the Senate presidency are Sens. Mary Kay Papen of Las Cruces, Linda Lopez of Albuquerque and Carlos Cisneros of Questa.
Papen, 80, said both Republicans and Democrats had encouraged her to seek the presidency.
Morales said he planned to speak with the others about his interest in the job and the need for party unity in the selection process.
Sen. Peter Wirth, D-Santa Fe, said the field of candidates seems fluid, changing by the week. He has but one hope at this stage.
"The challenge for me is finding someone in our caucus who can get 22 votes," Wirth said.
He said that would prevent "a fractured caucus," such as the one that developed four years ago. Cisneros wanted the Senate presidency, but lost out to Sen. Tim Jennings of Roswell.
Jennings won at the last minute on the basis of support from a group of Republicans and Democrats.
Sen. Timothy Keller, D-Albuquerque, said more can be accomplished if the Senate commits to a president from the majority party. This eliminates indecision and focuses the body on achieving clearly stated goals, Keller said.
"Really, the question is whether the majority caucus can coalesce around one candidate," Keller said.
Morales, a senator since January 2008, is a member of the Senate Finance Committee. He has had a hand in budgets during the end of a boom and an extended recession.
In the last two years, Morales has criticized and challenged Republican Gov. Susana Martinez's education initiatives more than any other legislator. He has focused in particular on the A-F grading system for public schools.
Morales says the grades are flawed, and that legislators need to fix the system before it demoralizes school staffs and students.
He also has been vigorous in reviewing government policies for practicality and effectiveness.
For instance, Morales said the system of legislative candidates filing nominating petitions was an unnecessary requirement that should be scrapped. Eight challenges to petitions filed by incumbent legislators went to the state Supreme Court last spring.
After all the lawyers' arguments and court time, everybody remained on the ballot.
The job of Senate president is open because Jennings, 62, was defeated in this month's general election. He will be succeeded by Cliff Pirtle, 27, a Republican from Roswell.