Blockbuster Inc. is asking creditors to put up more money to help it exit bankruptcy protection, prompting a debate among bondholders about whether to invest further in the struggling video chain or put it up for sale, people familiar with the matter said.

When Blockbuster filed for Chapter 11 protection in September, the company  had agreed to turn ownership over to its creditors. But after poor holiday sales and new estimates for a costlier turnaround, the company is asking bondholders for an additional $200 million to $250 million to be used after the chain exits court protection.

The discussions on the additional funds have just begun and the two sides haven’t determined a “hard number” for the desired amount, one of the people said.

The bondholders are led by billionaire investor Carl Icahn and hedge-fund Monarch Alternative Capital LP. The people familiar with the situation said a sale could be an alternative to giving Blockbuster more cash but that both sides remain focused on the company’s current plan and financing needs.

The chain also is considering closing hundreds more stores, the people added — up to 1,000 of the chain’s more than 5,000 remaining outlets. Blockbuster has closed about 1,000 locations the last two years. No final determination has been made, the people said.

Blockbuster, Icahn and Monarch didn’t respond to requests for comment.

A deadline passed Friday for Blockbuster to outline its reorganization plan, provide a business plan to bondholders and hire a chief executive. The two sides were in discussions to extend that deadline, the people said.

The CEO search, which has been on since late last year, is unlikely to be completed until Blockbuster “sorts out the capital structure and the ownership structure” of the company, one of the people familiar with the matter said.

Amid pressure from cable-television providers, Netflix Inc. and Internet entertainment outlets, Blockbuster generated 2010 earnings before interest, taxes, depreciation and amortization below $100 million, the people familiar with the matter said. That compares with more than $150 million in 2009.

The new cash and store closures would aim to give Blockbuster a liquidity cushion for the rest of the year as it tries to transition from a bricks-and-mortar operation to streaming films online. The company plans to emerge from bankruptcy nearly debt free by wiping out more than $900 million in obligations to bondholders and wants additional equity to drive its continued restructuring efforts, the people said.

Blockbuster is pinning its hopes on digital film delivery and expanded mail-order and kiosks to better compete with Netflix. It has deals with various partners to stream movies to cellphones and Blu-ray players, among other devices.

Still, Blockbuster lags far behind its biggest competitors. Blockbuster had 1.2 million subscribers to its DVD mailing service through the first nine months of last year, down from 1.5 million a year earlier. Netflix had 16.9 million subscribers in that time,  up from 11.1 million a year earlier.

Blockbuster’s need for more capital adds another wrinkle to a restructuring plan that was crafted just a few months ago.

Icahn supports providing Blockbuster with as much as $250 million, the people familiar with the matter said. Monarch is also inclined to invest more in Blockbuster, they said. Other hedge funds holding the company’s senior bonds are more reluctant to do that, the people said.

Amid these talks, bondholders have raised the prospect of putting Blockbuster up for sale, the people said. In that scenario, one of the bondholders, such as Icahn or Monarch, could emerge as a so-called stalking-horse bidder that sets a floor for bids in a bankruptcy-court auction. In a November regulatory filing, Blockbuster warned it couldn’t assure that bondholders would go along with its reorganization plan, which could force the company to put itself up for sale.

Blockbuster could fetch around $400 million or so in an auction based on where its senior bonds trade and the value of its inventory and real-estate, the people said.