STOCKHOLM, Sweden (AP) _ One of Swedens' wealthiest families offered Monday to buy the portion of Saab-Scania AB that it does not already own for nearly $2.3 billion in what would be one of the biggest corporate deals in Sweden.

The Wallenberg family already controls about 58 percent of the aerospace, truck and automobile group. Acting through family-controlled investment groups, Peter Wallenberg made a bid worth about 12.8 billion kronor, or $2.28 billion, for the rest of the company.

Saab-Scania said it would recommend that shareholders accept the bid.

Wallenberg offered to pay 300 kronor per share for Saab-Scania, which is almost 40 percent above the company's current price on the Stockholm stock exchange.

The bid was made through the investment company Patricia, owned jointly by the Wallenberg-controlled AB Investor and Forvaltnings AB Providentia.

Asked how he could afford it, Wallenberg, 64, said, ''It changes some of our numbers, but it does not shake us.'' He said he wanted to buy Saab-Scania partly because ''it has a long history with the family.''

The Wallenberg family has sold some assets and is borrowing on others to help pay for the deal. The dynasty reportedly has assets worth more than 1,000 billion kronor, or $178 billion.

Business analysts say the empire is too tightly stretched and is beginning to crack under the weight of its debt.

However, Wallenberg is positioning his empire for an eventual Swedish entry into the European Community.

The government plans to apply for membership this year. If membership is granted, sometime after 1994, laws guaranteeing Swedish citizens control of Swedish companies would have to be changed.

So Wallenberg may feel he has to consolidate his control.

He has had increasing difficulties maintaining the family's longtime hold over the nation's biggest companies, including telecommunication group Ericsson, ballbearing maker SKF, the paper-giant Stora and appliance maker Electrolux.

At the end of last month, Wallenberg sold his stake in Alfa-Laval, a food equipment maker, for 2.5 billion kronor, or about $446 million.

Business analysts suggest he may also be planning to sell off the poorly performing Saab car division to U.S.-based General Motors Corp., once he gains full control of Saab-Scania.

Saab-Scania and General Motors formed Saab Automobile as a joint venture in 1989. The automobile company lost 4.64 billion kronor, or $843.6 million, last year.

The Saab-Scania parent company, however, is expected to report earnings of 2 billion kronor, or $357 million, for 1990 due to truck and civilian aircraft sales. That's despite the delays and escalating costs of the JAS-Gripen, a new combat plane being developed for the Swedish air force.