Updates shares in paragraph 2, adds investor comment in paragraphs 9-10

By Yamini Kalia

June 25 (Reuters) - British budget carrier easyJet EZJ.L said it would grant U.S. investment firm Castlelake limited access to commercial data in hopes of drawing a higher takeover bid after rejecting a fourth sweetened £4.93 billion ($6.5 billion) proposal on Thursday.

Shares of easyJet, which operates more than 350 aircraft on over 1,200 routes in 37 countries, jumped by as much as 8% to around £5.80. However, they were still below Castlelake's latest offer of £6.50 per share.

The budget airline's board unanimously rejected the new proposal, saying it substantially undervalued the company, but said that giving Castlelake limited access to its books might produce a "more attractive proposal".

The latest 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".

Castlelake's deadline to table a firm offer has been extended to July 5 under UK takeover rules. EasyJet said that Castlelake had indicated it hoped to further improve its bid following limited access to the commercial information.

Castlelake said in a statement it welcomed the constructive engagement from the easyJet board and the deadline extension.

QUESTIONS OVER COMPLIANCE WITH EU OWNERSHIP RULES

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.

Samuel Ziff, a portfolio manager at Oldfield Partners, an easyJet investor, said that any new bid price would need to be "significantly higher" than the rejected proposal.

"EasyJet has got a very valuable fleet, they've got very valuable slots, and management has got this clear target that they want to hit by 2030 in terms of profitability," Ziff said.

Castlelake has also named New York-based Brookfield Asset Management BAM.N as a co-investor, 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. 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," analyst Shanley said, adding that concerns over ownership structure and an absence of a European airline investor might be ignored for the right price.

Brookfield was also part of a consortium that acquired one of the world's largest aircraft lessors Air Lease in a $7.4 billion cash deal last year.

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)