Though the Top Chef host announced her pregnancy in October, she was mum about the father's identity.
According to the source, Lakshmi, 39, and Dell, 40, are trying to work out visitation rights with their daughter, who will be a month old March 20. Dell would like "more time and involvement with the child," says the source. "It's all in negotiations. They are trying to work it out. They are trying to avoid anything messy."
Lakshmi, meanwhile, has been spotted recently with Krishna. On March 11, the two were photographed together on a New York City bench.
The baby's father was first reported by the New York Post.