Ms Ockenden said she had discussed the issue with bereaved families in Nottingham and said she “felt confident” there was a way that she could take on more without impacting the work she has done so far.
She said she would be willing to chair the inquiry in Leeds and a potential maternity review at University Hospitals Sussex NHS Trust, describing it as an “honour” to be considered.
The BBC has been told families in Nottingham are supportive of Ms Ockenden leading other reviews.
“We have to learn in this country that families shouldn’t have to fight as hard to get the answers that they deserve,” she said.
“We saw that at the start of the Nottingham review and we saw it in Shrewsbury and Telford, it’s not good enough.
“It’s always an honour and a privilege when families but trust in me and say they want me but it is not my decision, it’s for the secretary of state.”
She said nine families had been in contact with Streeting and asked for her to take on a potential review of University Hospitals Sussex NHS Foundation Trust – which has maternity units in Brighton, Chichester, Haywards Heath and Worthing.
Asked about calls for her to take on this work, she said: “Again the sentiments are the same, it’s an honour to be trusted by families, it is not my decision but there are ways it can be made to work.
“My promise, and I’ve discussed this in depth with Nottingham families and MPs, is it will not impact the quality or timeline for their review.”