FAR 61.1
Authorized instructor means—
(ii) A person who holds a flight instructor certificate issued under part 61 of this chapter and is in compliance with §61.197, when conducting ground training or flight training in accordance with the privileges and limitations of his or her flight instructor certificate; or
(iii) A person authorized by the Administrator to provide ground training or flight training under part 61, 121, 135, or 142 of this chapter when conducting ground training or flight training in accordance with that authority.
61.56
(a) Except as provided in paragraphs (b) and (f) of this section, a flight review consists of a minimum of 1 hour of flight training and 1 hour of ground training.
(c) Except as provided in paragraphs (d), (e), and (g) of this section, no person may act as pilot in command of an aircraft unless, since the beginning of the 24th calendar month before the month in which that pilot acts as pilot in command, that person has—
(1) Accomplished a flight review given in an aircraft for which that pilot is rated by an authorized instructor
§61.41 Flight training received from flight instructors not certificated by the FAA.
(a) A person may credit flight training toward the requirements of a pilot certificate or rating issued under this part, if that person received the training from:
(1) A flight instructor of an Armed Force in a program for training military pilots of either—
(i) The United States; or
(ii) A foreign contracting State to the Convention on International Civil Aviation.
(2) A flight instructor who is authorized to give such training by the licensing authority of a foreign contracting State to the Convention on International Civil Aviation, and the flight training is given outside the United States.
(b) A flight instructor described in paragraph (a) of this section is only authorized to give endorsements to show training given.
So you need an FAA authorized instructor for a flight review because a foreign instructor is unable to endorse the completion of a flight review and not authorized to endorse the ground training