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The model and actress - who has claimed Ryan is the father of the baby - welcomed a daughter named Kai into the world on July 1, with the Cruel Intentions actor reportedly by her side throughout the birth.
A source told US Magazine: "He is a good father, and whether this is his baby or not, he wants to do the right thing and be supportive.
"Alexis is really excited to be a mom."
While it has not yet been confirmed whether Ryan - who also has children Ava, 11, and seven-year-old Deacon with ex-wife Reese Witherspoon - is the father of the baby, Alexis has previously said she doesn't expect the actor to take responsibility for the child.
Her representative explained: "She has never asked Ryan for any help, nor does she expect it.
"Alexis has maintained her silence and will continue to do so. She continues to appreciate the love and support of her family and friends."
The Lincoln Lawyer star - who dated Alexis on and off for several months until September 2010 - is expected to undergo a paternity test to determine whether the child is his in the coming weeks.
