Adds shares in paragraph 2, analyst comments in 5 and 11

By Yamini Kalia

June 25 (Reuters) - British budget carrier easyJet EZJ.L rejected a fourth, sweetened £4.93 billion ($6.50 billion) takeover proposal from U.S.-based investment firm Castlelake on Thursday, but said it would grant the suitor limited access to commercial information in hopes of drawing a higher bid.

EasyJet shares rose nearly 6% to £5.7 in early trading.

The budget airline's board unanimously rejected the new proposal saying it continued to "substantially" undervalue the company, but it also believed that giving Castlelake access to limited commercial information might produce a "more attractive proposal".

The £6.50-per-share proposal was higher than Castlelake's previous £6.25-per-share offer. It is also tracking towards the £7 apiece price tag easyJet investors were hoping to get, according to a Financial Times report from last week.

"The narrative has definitively changed," said Dudley Shanley, an analyst with Goodbody Stockbrokers. EasyJet "are now effectively in negotiations with Castlelake, which means the business is for sale at the right price," he said.

Castlelake said it hopes to further improve its bid following limited access to the commercial information.

OWNERSHIP CONCERNS

Analysts had questioned whether Castlelake could structure a deal that would comply with European Union ownership rules requiring carriers to be majority EU -owned and -controlled, while also satisfying easyJet investors on price.

Castlelake on Thursday also added New York-based asset manager Brookfield Asset Management to the bidders, along with two previously disclosed partners, former Malaysia Airlines CEO Peter Bellew and senior industry executive Mark Breen.

Under the proposed terms, the bidding vehicle would be owned 49% by Castlelake and co-investors including Brookfield Asset Management BAM.N. The remaining 51% would be owned by EU nationals Bellew and Breen.

"The reality is price is much more important than who's actually buying," Shanley said, adding that concerns over ownership structure and an absence of a European airline investor might be swept under the rug for the right price.

Castlelake's deadline to table a firm offer has been extended to July 5 under UK takeover rules.

EasyJet, which competes with other low-cost carriers such as Ryanair, last month warned its full-year forecast remained uncertain as the Iran conflict drove up fuel costs, while summer bookings were behind last year.

($1 = 0.7590 pounds)