Ms Obama said she would “have to see” when asked if she hoped Mr Biden would run again in 2024, during an ABC News special that aired on Sunday.
She said it was a personal decision that he and his wife Jill Biden would have to make.
“Probably, if I hadn’t been through it, I would feel more cavalier about opining on it,” she said.
“But I know it’s a personal call and I don’t want to be one of the millions of people weighing in on what he should do, he and Jill should do.”
The former first lady added that Mr Biden is “doing the best he can.”
“It’s probably the only job that few people know what it feels like to do, but everybody thinks they know how to do it. Everybody’s a backseat driver when it comes to being Commander in Chief of the most powerful nation on earth,” said Ms Obama. “But it’s a tough job and I think that he’s doing the best he can under some tough circumstances.”
At 79, Mr Biden is the oldest president in American history, and questions are swirling over his political future.
In September Mr Biden said it was “much too early” to make the decision on whether he would run again, opening the door to potentially not seeking another term.
And last month, the president said he has not made a formal decision, but called it his “intention” to do so.
Ms Obama is promoting her new book, The Light We Carry: Overcoming in Uncertain Times, which covers her time leaving office in an uncertain political climate and feeling lonely during the pandemic.
During the midterm election campaign, Mr Biden said that if Democrats picked up seats, the first piece of legislation that he would send to Congress would be to enact a nationwide right to abortion.
The right was previously guaranteed only by the US Supreme Court in the landmark 1973 Roe v. Wade decision, and the court’s conservative majority overturned that ruling earlier this year.
Although Democrats defied historical odds by avoiding a midterm wipeout, they appear not to have gained enough ground to ensure abortion access nationwide.
Asked what voters might expect on the issue, Mr Biden replied: “I don’t think they can expect much of anything.”
Although ballots are still being counted, Republicans are on track to take control of the House of Representatives by a narrow margin, putting them in position to block any abortion legislation.
“I think it’s gonna be very close, but I don’t think we’re gonna make it,” Mr Biden said.