Two high-ranking government officials said yesterday that they expect a settlement next week of U.S. Steel Corp's dumping cases against steel makers in seven European countries.

U.S. Steel and government negotiators have been meeting off and on for weeks and are near a settlement, although a few stumbling blocks remain, the officials said.

They wouldn't disclose those problem areas.

The settlement revolves around modification of the trigger-price mechanism which is supposed to automatically initiate an investigation by the government of dumping cases when steel products are shipped here below specified prices, sources said.

The steel industry, however, hs said that the trigger-price mechanism is ineffective in preventing foreign countries from dumping, that is, selling goods in the United States below their costs of production, thereby injuring U.S. markets.

The trigger-price mechanism generally is adjusted every quarter to reflect market conditions. However, the government refused to raise the trigger-price mechanism during the second quarter this year. Shortly thereafter, U.S. Steel cases have been a problem area for the Carter administration because they heightened tension between the United States and the European Economic Community. Relations already were strained by other trade disputes, and the EEC has veremently denied that its steel producers are dumping.

The president has setup a tri-partite committee to develop a policy to aid the ailing steel industry. The government officials said those talks are separate from the U.S. Steel negotiations although they both concern the trigger-price mechanism. A steel policy is expected from Carter within days, sources said.

The high-ranking officials said announcement of the settlement probably will be made by U.S. Steel. However, spokesmen for the nation's largest steel producer have maintained publicly that the company isn't settling the cases.

"There's been a lot of speculation about [the settlement] but we haven't made any statements on that at all," a U.S. Steel spokesman said earlier this week. U.S. Steel "has not asked for anything beyond resolution of the dumping cases, the spokesman added.

Another U.S. Steel spokesman said the company plans to go ahead with dumping cases against Japan and Canada, but said he doedn't know when those cases would be filed.