J.C. Penney Co Inc (JCP.N) has started looking for a new chief executive officer to replace Myron Ullman and top investor Bill Ackman has pushed the board to have one named within 30 to 45 days, CNBC reported on Thursday.

Ackman, frustrated by the pace of the CEO search, also said former Penney CEO Allen Questrom had conditionally agreed to rejoin the company as its chairman, CNBC reported.

J.C. Penney, Ackman and Questrom could not immediately be reached for comment.

Shares of J.C. Penney jumped 5.3 percent to $13.64 following CNBC's report.

Ullman, CEO from 2004 to 2011, was brought back in April to stem a sales hemorrhage resulting from ex-CEO Ron Johnson's failed attempt to make the 111 year-old retailer a trendier department store. On his watch, sales fell 25 percent last fiscal year as shoppers rejected his no-discounts pricing strategy.

Ullman's return was praised in April as a smart move to repair relations with Penney's vendors and lift the morale at the company. He has largely brought back the strategy Johnson jettisoned, resorting to deep and frequent promotions, moves that some analysts say are not working fast enough.

Penney shares earlier this week hit their lowest levels since 2001 and several analysts downgraded their ratings on the stock. Analysts expect Penney to report same-store sales fell 7 percent this quarter when it releases quarterly results on August 20.

Johnson became CEO in 2011, handpicked by Ackman, who nearly a year earlier had taken an 18 percent stake in Penney and started pushing for Ullman's ouster and a new strategy to reach younger shoppers.

In addition to the long struggle to win back shoppers alienated by Johnson's strategy, Ullman has had to contend with big holes in his management team. Only this week did Penney name a new marketing head after the role was vacant for 14 months. No one is currently heading its home goods section.

Questrom said on CNBC that a new chief would need to have CEO experience, unlike Johnson whose highest position before joining Penney was head of retail at Apple Inc.

But some experts said another round of change at the top could hurt Penney at a time that it is preparing for the holiday season, when many analysts expect it will finally begin to see sales recover.

"A new CEO would be disruptive because that would bring more change," said Walter Loeb, a veteran retail analyst, who said shoppers are beginning to come back to Penney.

Questrom, a respected retailer, said however that Penney's board needs to act quickly and that he would only return as chairman if he was comfortable with the new CEO.

"They certainly don't have a sense of urgency and if I had a company that was in this kind of trouble I'd be much quicker to make a decision," he told CNBC.