Financier Victor Posner's Sharon Steel Corp., apparently unable to make $38.5 million in interest payments on a number of its outstanding debentures, said yesterday that it will ask holders of the notes to accept new securities in exchange for some of them while the company sells assets to raise money to pay off its debts.

The troubled company, one of the cornerstones of Posner's farflung financial empire, also said that it expects to report $145 million in losses for 1984.

Sharon Steel's woes have raised questions about the financial soundness of the rest of Posner's holdings, particularly because Evans Products Co., another company in which Posner has a major holding, recently filed for bankruptcy. Spokesmen for the Miami Beach-based financier have insisted, however, that these problems aren't related to, and don't reflect on the state of, the rest of the Posner empire.

Posner owns 40 percent of NVF Co., the parent company of Sharon Steel. Sharon, in turn, holds 43 percent of Evans Products.

Sharon Steel missed a $23 million interest payment March 1 on its 13 1/2 percent subordinated sinking fund debentures, and had to make the payment by yesterday to avoid going into default. Yesterday, Sharon said it also does not expect to be able to make another interest payment, of about $4.3 million, due April 15 on its 14 1/4 percent subordinated sinking fund debentures.

In addition, Sharon indicated that it would have to make other arrangements to pay $10.8 million in interest on a third debt issue that came due last Friday.

Instead of making the payments, Sharon proposed yesterday to give holders of the 13 1/2 percent and 14 1/4 percent debentures a package of securities that would include stock in the company and secured debentures.

To pay the additional $10.8 million interest expense that came due last week, Sharon said it would ask its banks for permission to sell some of its assets to make the payment.