Among the strategies it is discussing is structuring the potential transaction so that Allergan would technically be the buyer, according to a person briefed on the matter who spoke on the condition of anonymity. Because Allergan’s headquarters are already in Ireland — even though much of its operation is based in New Jersey — the arrangement could allow the deal to avoid being deemed an inversion.

Yet in reality, Pfizer, with a market value of about $205 billion, would still effectively be buying its counterpart, which has a capitalization of about $124 billion. Its shareholders would own more than 55 percent of the combined company, and Allergan’s shareholders would receive a premium for their holdings, the person added.

A deal could be reached in a little over a week, the person said, cautioning that talks are continuing and may still fall apart.

Representatives for Pfizer and Allergan declined to comment.

Reaction to the rules, which were released late in the afternoon, was muted. Stephen E. Shay, a senior lecturer at Harvard Law School, said they were weaker than many people expected. “It’s not going to do anything to affect in any meaningful way the largest deal that is in front of them,” he said.

Laurence M. Bambino, the head of the global tax group at the law firm Shearman & Sterling, said: “It’s another misguided attempt by Treasury to box in U.S. corporations to the benefit of non-U.S. corporations.”