"It looks like LeBron James is working to do good things on behalf of our next generation and just as she always has, the First Lady encourages everyone to have an open dialogue about issues facing children today," Melania said in a statement released by her spokeswoman.
"As you know, Mrs Trump has traveled the country and world talking to children about their well-being, healthy living, and the importance of responsible online behavior with her Be Best initiative," the statement continued.
"Her platform centers around visiting organizations, hospitals and schools, and she would be open to visiting the I Promise School in Akron," the statement said.
On Friday the US president had taken to Twitter to slam the basketball player after his appearance where LeBron had said the US leader was using "sports to kinda divide us."
"Lebron James was just interviewed by the dumbest man on television, Don Lemon. He made Lebron look smart, which isn't easy to do. I like Mike!" Trump posted.
Trump is often seen criticising the National Football League (NFL) for not punishing its players who protest by refusing to stand during the national anthem at football games.
LeBron, who has slammed the president in the past, also said he "would never sit across" from the US leader, adding, "I'd sit across from Barack Obama though."
The basketball player is yet to weigh in on the debate.