"Rumors are that both the Knicks and the Nets would like to get him. I would never take sides on that, but I think it would be great for New York if he would come here," Bloomberg said on his weekly Friday show on WOR Radio.
The two-time MVP will be the most-coveted prize when the NBA's free agency period starts July 1.
One Twitter posting said, "Can we change the Bronx to LeBronx? Pretty please, at least until July 1." The mayor's office happily retweeted it, adding: "Good one!"
James and the Cavaliers fell short again in their effort to bring a title to Cleveland, getting eliminated from the Eastern Conference playoffs Thursday by the Boston Celtics, and fueling speculation that James' days with the Cavs are over.
"If asked, if he calls me and says 'What's it like to live in New York?' I'll give him a big sales pitch for New York,' " Bloomberg said on his show.
"I love living in New York, my kids love living in New York, I think LeBron James would love living in New York and it is the world's greatest stage," the mayor added.
Meanwhile, a music video posted on Break.com features Clevelanders and Ohio Gov. Ted Strickland in a sing-along to the tune of "We Are the World." The song's lyrics include, "Please stay, LeBron. We really need you. No bigger market's gonna love you half as much as we do."
It also took a shot at New York City, with lyrics "New York's overcrowded. Those people are unbearable. And don't forget, the Knicks and Nets are terrible."
James grew up in Akron, Ohio, less than an hour's drive south of Cleveland.
Akron Mayor Don Plusquellic elaborated to The Associated Press on his comments in Friday's New York Daily News, where he was quoted as saying, "Who the hell would want to live in New York?"
Plusquellic said he was joking and responded in jest to a reporter's line of questioning about why James would want to stay in Cleveland.
He said he was sticking up for Akron and the rest of Ohio, which he called a great place to raise a family.
"It's not a cold place where everybody is just a number," Plusquellic said, adding that "New York is not so warm and fuzzy."
Plusquellic said he attended the opening Friday of a new restaurant at the city's minor league ballpark, where the locals appreciated his comments.
"No one here is going to find fault with what I said," he said. "I know a few folks in New York were probably upset. The mayor [Bloomberg] hasn't called or anything."