The battle for Paramount Communications enters its critical stages today.After three months of desperately trying to consummate its proposed marriage to Viacom Inc., Par’s board of directors will this afternoon accept bids in the auction of the entertainment giant. But as usual with closed-bid auctions, the sale process really begins with the submission of offers. While the board says it intends to evaluate the proposals on a timely basis, they must remain open through Jan. 7. And Par retains the right to negotiate further with all suitors once the bids are received, and that includes working to increase the price. Some sources said it could be mid-January before a winner is declared. On Friday, Par rejected QVC’s recommendation that the auction be open and public with bidding continuing until the highest bid is received. Par said QVC’s “notion of open and public bidding will risk failing to achieve the best possible value to Paramount stockholders.” The company also sent a clear message to suitors that they better have their best offers on the table today, saying it would need to consider “lockup agreements” with a winning bidder — an indication that the low bidder today may not get a second chance. Further, Par warned, “Any failure of QVC to submit its best and highest bid is at its own risk.” QVC chairman Barry Diller said he will go along with the board’s procedures and seek relief from the courts if he feels QVC is not being treated fairly. Sources said QVC and Viacom spent the weekend with their financial advisers and backers working to develop their formal bids. Sources close to Viacom said the company has spoken to backers Blockbuster Entertainment and Nynex about ponying up more dough, though Viacom denied comment. QVC is said to be talking with partner BellSouth for the same reason. But both companies are said to be reluctant to cede any more control. While the auction could set off another round of escalating bids, most believe the offers will not be that much higher than what’s already on the table. “The hope of a big windfall is overly optimistic in this case,” said analyst Edward Hatch of UBS Securities. “We’ve been suggesting that investors sell into these optimistic rallies. If you like the combined company, buy it later in the open market at what will probably be a lesser price.” Heading into the auction, QVC’s standing offer was valued at about $ 10 billion, or $ 84.06 a share. Viacom’s offer — which has trailed QVC’s by as much as $ 1 billion in recent weeks — has significantly closed the gap. Helped by a buy recommendation from brokerage Salomon Bros., Viacom’s offer was valued at about $ 9.5 billion, or $ 80.38 a share, based on Friday’s closing stock prices. Separately, Par, QVC and Viacom agreed to take no action for now on the $ 100 million termination fee Par agreed to pay Viacom if it fails to acquire the company. Shareholder attorney Arthur Abbey said a motion filed last week asking the Delaware Chancery Court to enjoin the fee “has been put on hold pending the outcome of the bidding auction.” Separately, Viacom chair Sumner Redstone, in a statement Sunday, said his National Amusements Inc.’s buys of Viacom stock in July and August were “totally lawful and appropriate.” He also said he had no influence over WMS Industries Inc., which bought Viacom stock during the Par bidding war. Redstone holds a 24. 9% stake in WMS.