The Hollywood star walked out on James earlier this month after tattoo model Michelle McGee went public with claims she romanced the married reality star for 11 months, including a period when Bullock was shooting "The Blind Side" on location.
A string of other women have since come forward with allegations of affairs with James.
The TV mechanic's ex-wife, Janine Lindemulder, spoke out after the scandal broke, insisting she wanted Bullock to remain close to her daughter Sunny, 6.
She said, "If Sandra decides to keep a relationship going with our daughter Sunny, I would in no way stop that. Sunny loves Sandy and vice versa. She's welcome to be a part of every aspect of Sunny's life. She has taken care of our daughter as if she was her own ... She sacrificed much ... and I will forever be indebted to her for that."
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Lindemulder's comments sparked speculation that the actress was preparing a bid to legally adopt James' daughter, as well as his two other children from a previous relationship, but her rep has moved swiftly to shoot down the rumor.
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Bullock's spokesperson tells People.com, "There are no plans, nor have there ever been any plans, for Sandra Bullock to adopt any of Jesse James' children."