The 35-year-old model - who met the 'Catwoman' actress in 2005 on a photoshoot for Italian fashion house Versace - entered papers at Los Angeles Superior Court on December 30 requesting the recognition.
Gabriel , who split with the 44-year-old star in April 2010, is also seeking to establish physical and legal custody of the child, whose surname is already registered as Aubry.
Oscar-winning beauty Halle has previously stated she would quit acting if it was in the best interest of her daughter.
She said: "Children shift your priorities and now I have a greater purpose for being here. I love making movies but I would give it all up to be with my daughter if I had to because she's the love of my life. "She's made me a better person because everything I do and say, everything I want and don't want, I think first, 'Will this be best for her?'
"When you have children you get to see things all over again. So I've never laughed as hard, I've never done more silly things, and I go to great lengths to make her laugh. She's awakened a childlike side of me."