"I have a newborn!" Lakshmi tells PEOPLE. "I just want some peace and privacy."
Since she announced she was pregnant in October, Lakshmi has remained mum about the identity of Krishna's dad, but a source close to her admits it is indeed Dell, a venture capitalist.
"They had an on-and-off minimal relationship that ended many, many months ago," says the source.
The source also calls an earlier report that the two are trying to work out visitation rights "inaccurate."
"There already is a very fair agreement in place," says the source. "She doesn't want anything from him. She's juggling all of this with motherhood and preparing to go back to work and it's a lot to handle."