Istanbul's chief prosecutor is investigating Tolga Tanis, who is based in Washington, after Erdogan's lawyer Ahmet Ozel filed a petition accusing him of undermining the reputation of the president.
It appears to fit in with a fresh wave of legal activity by the embattled Turkish president, who has attempted to sue dozens of journalists and activists for damage to his reputation.
According to Hurriyet, Ozel claimed that the book contained false information that "could undermine the reputation of, and provoke the public against" his client.
Tanis's book, called Potus and the Gentleman, gives an analysis of the relationship between US President Barack Obama (Potus is an acronym for President of the United States) and Erdogan, who is sometimes referred to as "the gentleman" by allies.
Tanis says that in his book he was critical of both Erdogan and Obama, but that after reading the complaint he still does not know what Erdogan's lawyer considers to be untrue in his book.
"All they are saying that the book is untrue, provocative, or targeting the reputation of the President, but they are not stating why," he claimed.
Tanis says the complaint focused on a story about oil deals between the Kurdistan Regional Government in Northern Iraq and a group of firms registered in the British Virgin Islands. The book, he claimed, reveals for the first time ties between those companies and Erdogan's son-in-law.
"I am critical of both Erdogan and Obama on several issues. For example I very harshly criticize President Obama, especially on Syria policy, and accuse the United States administration of being hypocritical. Though it was only Erdogan who sued me,'' said Tanis.
Erdogan's government has placed numerous constraints on freedom of the press. When a 2013 corruption probe alleged that four former ministers from Erdogan's AK party were involved in graft, the government issued a gag order preventing journalists from reporting on the probe's findings.
Dozens of those who decided to report on the probe were subsequently sued.
The Committee to Protect Journalists has condemned the 21-month suspended prison sentence given to Bulent Kenes, editor-in-chief of the newspaper Today's Zaman, for posting a critical comment on his Twitter account in July 2014. Prosecutors said he had insulted the president.
The European Parliament expressed concern over Erdogan's aggressive stance towards the press in December 2014. The Reporters Without Borders Press Freedom Index 2015, which analyses media freedom in 180 countries worldwide, ranks Turkey at number 149.
However, Erdogan has claimed that Turkey's press is free.
Reuters reported that Erdogan's lawyer and the prosecutor's office could not be reached for comment.
