The operator of Carl’s Jr. and Hardee’s restaurants said Wednesday it may have received a better takeover offer than the one it already has from a private equity firm.

CKE Restaurants Inc. said an unnamed party submitted a bid that may be superior to its current deal with Thomas H. Lee Partners, a Boston firm that’s among a trio of investment firms that bought Dunkin’ Brands Inc. in 2006.

The news sent the company’s stock up 75 cents, or 7 percent, to $11.83 in premarket trading. The shares have traded between $7.60 and $11.57 over the last year.

CKE accepted Lee’s offer in February, which includes about $619 million in cash and approximately $309 million in debt.

Under terms of the deal, CKE shareholders would receive $11.05 in cash for each share they own.

CKE did not disclose many specifics about the new proposal, but said it can keep talking with the bidder until April 27 because of terms in the agreement with Thomas H. Lee. The bidder did not disclose how they would pay for the transaction.

CKE was allowed to seek alternative offers until Tuesday. Back in February the restaurant operator, based in Carpinteria, Calif., said it wouldn’t disclose any information related to its talks with other potential buyers — unless its board decided that a superior bid had been received.

Representatives for CKE and Thomas H. Lee couldn’t immediately be reached for a comment.

Business for CKE and many of its competitors slowed during the recession and kept some of its most loyal customers — young men — away from its restaurants.

CKE reported late last month that its fourth-quarter profit grew, but it was mostly due to a sizable tax benefit. The restaurant operator’s revenue fell nearly 5 percent during the quarter, while sales at stores open at least a year dropped 6 percent. This figure is considered a key performance indicator because it measures growth from existing locations rather than newly opened ones.

For the full year, CKE’s profit climbed 30 percent as annual revenue slipped 4 percent.

The company operates and franchises 3,141 restaurants in 42 states.

Other related reading at Carl’s Jr. Owner CKE Bought by Thomas H. Lee Partners  and Other buyers interested in CKE?