Nogueira, 37, failed to make it out of the first round against Nelson at a UFC Fight Night event in Abu Dhabi. He was knocked cold by a right hand at the 3:37 mark. It was the fifth time Nogueira (34-9-1) has been stopped in his past eight fights.
The former Pride champion has since stated a desire to face Frank Mir a third time before hanging up his gloves. Nogueira lost to Mir in 2008 and 2011.
On Wednesday, White said he'd prefer to see Nogueira retire immediately.
"He is a warhorse," White said. "The battles in Pride he's been in, let alone the fights he fought in the UFC. He's one of the most respected fighters in the world by other fighters, let alone fans.
"I wanted to give him the opportunity to say something first and now I'm going to say, 'Big Nog, I love you -- but I'd love you to never fight again.'"
Nogueira fought nearly 10 years before he was stopped for the first time -- by Mir via TKO at UFC 92. He is 3-5 in his last eight bouts and has undergone surgeries on his knees, hips and arm.
Whether or not the Brazilian eventually agrees with White is yet to be seen. Prior to the Nelson loss, Nogueira acknowledged to ESPN.com that he might be nearing the end of his career.
"Let's see what I can still show," Nogueira said. "If I'm not showing well or I'm not motivated, there is no way I can be fighting anymore."