"I've been approached, yes. I'm taking a look at it — a serious look at it," Sanchez said Thursday in an interview.
Sanchez, D-Belen, said entering the race would be "an interesting proposition" because of a climate of negative campaigning.
"Democrats need a viable candidate who is capable of standing up to the pressure," he said.
Republican Gov. Susana Martinez, a critic of Sanchez, targeted him for defeat in last year's legislative elections. Her campaign committees hit Sanchez with a series of ads saying he was soft on child killers.
Sanchez, 62, answered back in television ads featuring him and his wife, Lynn. He routed Republican David Chavez in the Senate race.
State Sen. Timothy Keller, D-Albuquerque, said Sanchez's victory was perhaps Martinez's worst moment in the 2012 elections.
"She shot an air ball against Michael," said Keller, another of those considering whether to enter the race for governor.
Sanchez said he would decide no later than June whether to form an exploratory committee. Anybody who wants to run will have to act quickly because of fundraising demands, he said.
"If you're getting in, you can't wait too long. At a minimum, it will take $3 million, and that's a pretty conservative estimate," Sanchez said.
State Attorney General Gary King and state Sen. Linda Lopez of Albuquerque are the only Democrats who have committed to running for governor.
Keller, Sanchez and Sen. Howie Morales of Silver City are the others who have said they may run.
"Michael would be tough to beat in a primary," Morales said.
An attorney, Sanchez has been in the Senate for 21 years. Martinez publicly criticized him in 2011, saying he was intentionally holding up legislation she wanted to retain thousands of third-graders if they did not read proficiently.
This year, Martinez publicly thanked Sanchez for carrying a couple of noncontroversial bills that she favored.
But for the second year in succession, Martinez also vetoed a bill by Sanchez to expunge certain criminal records.
Their relationship has been icy, especially during last year's campaign when Martinez hoped that Chavez would wrest away Sanchez's Senate seat.
Sanchez, like many Democrats in the Legislature, said at the time that Martinez showed no interest in bipartisanship and instead took a "my-way-or-the-highway" approach to governing.
"The governor's attitude has been, her pieces of legislation are perfect, or her proposals are perfect," Sanchez said during the campaign.
As Senate majority leader, Sanchez is probably the most powerful of New Mexico's 112 legislators. He controls the Senate calendar and decides which bills will get votes on the floor.
Sanchez, like all state senators, will be at mid-term during the 2014 election. He would still keep his Senate seat if he ran for governor and lost.
Milan Simonich, Santa Fe bureau chief of Texas-New Mexico Newspapers, can be reached at email@example.com or 505-820-6898. His blog is at nmcapitolreport.com.