Adds details on proposal from paragraph 3

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.

"The Board believes that giving Castlelake access to limited commercial information, as Castlelake sought in the letter which contained the Fourth Proposal, might produce a more attractive proposal," easyJet said in a statement.

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.

EasyJet's board unanimously rejected the new proposal, saying it continues to "substantially" undervalue the company, among other issues.

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

The U.S. firm has added New York-based asset manager Brookfield Asset Management to the bidding vehicle, 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.

To maintain an EU operating licence, European carriers must under EU rules be majority EU-owned and controlled.

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

($1 = 0.7590 pounds)