Target is still not able to estimate the cost of the data breach that affected tens of millions of customer's credit cards, and may not know until late in the second quarter or early third quarter, interim CEO John Mulligan told CNBC's "Street Signs" on Wednesday.

"We're in a place when it comes to the data breach where we don't have visibility yet to potential third-party liabilities and operating expenses they've incurred," said Mulligan, also the company's chief financial officer.