NEW YORK (CNN/Money) - Talks continue between Adelphia Communications Corp. and the former heads of the cable TV company, the Rigas family, about transferring some assets back to the company even as some members have been asked by the board to relinquish their seats, newspapers reported Tuesday.

The cable company has asked members of the Rigas family, its founders, to return about $2 billion back to the company to help offset $2.3 billion the family borrowed last year, the Wall Street Journal reported.

The Coudersport, Pa.-based company is teetering on the edge of bankruptcy ahead of its scheduled June 15 deadline to return $50 billion to bondholders or risk default.

The Rigas family is expected to return some stock it bought last year, which has depreciated since the family disclosed it borrowed $1.4 billion from Adelphia to purchase the shares, people close to the situation told the Journal. The family is also expected to give the company $1.2 billion in cable TV assets and about $600 million in convertible notes.

The negotiations are still underway and agreement could be reached this week, people close to the situation said, according to the report.

Rigas family members, who controls five of the nine seats on Adelphia's board, also have resisted stepping down and giving up their majority stake in voting rights, according to a New York Times report Tuesday.

While John Rigas stepped down from his CEO post and son, Timothy, also resigned from the company, both have remained on the board.

Adelphia could not be immediately reached for comment.

Adelphia is under investigation by the Justice Department and the Securities and Exchange Commission for some off-balance sheet transactions, including a $2.3 billion loan given to the Rigas family. Some of that money may have been used to fund a golf course, acquire some land and timber rights, and to buy part of the Buffalo Sabres hockey team, the Journal said.

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John Rigas could invoke his Fifth Amendment rights when asked to testify about the family's finances, people close to the situation said, according to the Times report.

The company is scheduled to meet with Nasdaq officials again Tuesday about whether the company should be delisted.

Shares of Adelphia (ADLAE: Research, Estimates) have not traded since developments involving the Rigas unfolded last week. They last traded at $5.69 on May 15.