Jackson made his request Sunday, several hours after Teixeira called him out at UFC 153 in Rio de Janeiro.
“Yo [Dana White], set up that fight with Glover please!” Jackson said on Twitter. “Let’s give him what he wants.
“Fans, I won’t let you down.”
Teixeira let his desire to fight Jackson be known minutes after defeating Fabio Maldonado by second-round TKO.
“I’d like to fight Quinton Jackson,” Teixeira said after improving to 19-2. “I never talked [smack] about him. He was my idol.
“I loved that guy coming up in Pride. But he says I was talking bad about him. I’m not talking bad about him. I’m not afraid of no man. Step in the ring with me; I’ll fight anyone.”
White was not specific about the next opponent for Teixeira -- the hard-hitting native of Brazil who now calls Danbury, Conn., home -- but it won’t be current light heavyweight champion Jon Jones.
“[Teixeira] is going to have to fight one of the top guys before we start talking about title shots,” White said.
Teixeira was scheduled to fight Jackson at UFC 153, but Jackson was forced to pull out of the bout after suffering an undisclosed injury during training. Maldonado then stepped in for Jackson.