There were concerns inside the company, Psy-Group, about the plan’s legality, according to one person familiar with the effort. The company, whose motto is “shape reality,” consulted an American law firm, and was told that it would be illegal if any non-Americans were involved in the effort.

Mr. Zamel, the founder of Psy-Group and one of its owners, has been questioned about the August 2016 meeting by investigators for the special counsel, and at least two F.B.I. agents working on the inquiry have traveled to Israel to interview employees of the company who worked on the proposal.