You will need TSA approval for any flight training. See below,
Who must participate in the Alien Flight Student Program?
Persons seeking flight training must submit a request if they are not citizens or nationals of the U.S. and:
- They wish to receive flight training in the U.S. or its territories, regardless of whether training will lead to an FAA certificate or type rating; and/or
- They wish to receive flight training from an FAA-certificated facility, provider, or instructor that could lead to an FAA rating whether in the U.S. or abroad.