Several major tax fraud investigations involving millions of dollars may be dropped by the Justice Department this week.

Sources close to Project Haven - a decade-long probe by the Justice Department and the Internal Revenue Service into the use of offshore tax havens by wealthy Americans seeking to evade tax payments - say that in some of the cases the government is letting the statute of limitations expire this week.

As the tax filing date passes tomorrow midnight, the government loses jurisdiction over tax fraud involving 1971 returns because of a six-year statute on prosecuting tax fraud.

That probe became controversial last year when a federal judge in Cleveland ruled that informants for the IRS acted improperly when they consipired to acquire documents from Bahamian bank official Michael Wolstencroft earlier in the investigation.

While a female informant took the Castle Bank & Trust official to dinner in Key Biscayne, Fla., in January 1973, another informant entered her apartment and removed a crucial list of account holders from his briefcase, which had been left there.

He took the list of Castle account holders to waiting IRS agents. The agents photographed the list, and the informant returned the list to the briefcase before the Nassau bank official returned from dinner.

The list gave the government several crucial leads, "breaking the case wide open," according to one IRS agent. Another incident, involving a Rolodex card file taken from the now defunct bank itself, provided confirmation on many of the names.

But U.S. District Court Judge John M. Manos, hearing the government's case against one of the alleged tax evaders in Cleveland, ruled that the briefcase capper, as it came to be known, was illegal, and any evidence from it used to prosecute would be deemed "tainted," or not acceptable in court.

The government appealed the ruling, but last month a three-judge panel of the 6th U.S. Circuit Court of Appeals upheld Manos' ruling.

However, many of the Project Haven cases were developed independent of the briefcase capper, and Justice Department and IRS probers had hoped to bring them to trial. Other cases, notably involving some prominent Chicago tax attorneys, have resulted in convictions.

Several cases were due for action in recent months, but according to knowledgeable sources "were not pushed because the heat has gone off Project Haven, and the department thinks that it doesn't help its image to push the cases."

Of four pending cases, none may make it to indictment, "because they are worried about the briefcase image," said one source.

Two of the cases being developed, according to sources, concern a Chicago tax attorney and a large Florida construction firm. Both will probably be dropped because they can be linked with the briefcase.

But two other cases that are reportedly not linked with the briefcase now may also be dropped.

One Florida case, according to the sources, involves more than $8 million in unreported income by Toyota Motor Co. officials.

The case is reportedly similar to one brought in Los Angeles in 1976 against several Toyota of America officials there who were charged with accepting kickbacks from persons seeking automobile distributorships. The alleged kickbacks had been paid through castle Bank to disguise the source of the payments.

And a second case that, according to one source, may also be lost "in a matter of days" if no action is taken, involves commodities transactions in Chicago that may have been bogus, with illegal profits allegedly being laundered through Castle.

Justice Department officials would not comment on Project Haven or any pending cases. But one attorney working on the cases said that if a taxpayer filed a 1971 return late, it would fall under Justice Department jurisdiction until the sixth anniversary of its filing.