In fact, Democratic candidate for president Hillary Clinton was recently asked about the very possibility of nominating President Obama as a Supreme Court justice. Here's Alex Seitz-Wald writing on MSNBC:
At a town hall meeting here five days before the Iowa caucuses, a voter asked the Democratic presidential candidate if she would be open to nominating Obama, a former constitutional law professor and president of the Harvard Law Review, to the nation’s highest court. Clinton laughed and marveled that no one had ever asked that question.“That’s a great idea,” she said, noting that the next president may be able to appoint as many as four justices. “I would certainly take that under advisement. I mean, he is brilliant and he can set forth an argument.”
As it happens, Obama himself has weighed in on the possibility before, making clear he's not that interested in the job. Here's what he told the New Yorker in 2014:
“When I got out of law school, I chose not to clerk,” he said. “Partly because I was an older student, but partly because I don’t think I have the temperament to sit in a chamber and write opinions.” But he sounded tempted by the idea.“I love the law, intellectually,” Obama went on. “I love nutting out these problems, wrestling with these arguments. I love teaching. I miss the classroom and engaging with students. But I think being a Justice is a little bit too monastic for me. Particularly after having spent six years and what will be eight years in this bubble, I think I need to get outside a little bit more.”
There's a precedent of a president becoming a Supreme Court justice after his term in the White House. William Howard Taft, who served as president from 1909 to 1913, joined the Supreme Court eight years later, nominated by Warren Harding, and served from 1921 to 1930.