Marquardt (28-8-2) stopped American Top Team's Wilson Gouveia in the third round, while Maia (10-0) submitted uncrowned WEC middleweight champ Chael Sonnen with a triangle choke in the opening frame.
"Last fight I [said] that I was just waiting, that I was just step-by-step, but now if I have the chance, I want to fight for the title," Maia said in the post-fight conference. "I won five fights by submission. I deserve to fight [for the belt] but of course it doesn't depend on me, but I want to fight for sure. I feel prepared right now psychologically, physically and technically."
Marquardt, who has won three of four since getting stopped by champion Anderson Silva at UFC 73 in July 2007, says a title shot would be ideal but would also be happy to take on Maia.
"My last three, four fights have shown that I deserve a title shot but if I need to face Demian first, that'll be great," Marquardt said.
Silva is scheduled to defend his belt next against Thales Leites -- Marquardt's most recent loss -- at UFC 97 "Redemption" on April 18 in Montreal, Canada.