WASHINGTON—The White House is expected to send guidance to the Pentagon in coming days on how to implement a new administration ban on transgender people in the military, issuing a policy that will allow Defense Secretary Jim Mattis to consider a service member’s ability to deploy in deciding whether to kick them out of the military.

The White House memo also directs the Pentagon to deny admittance to transgender individuals and to stop spending on medical treatment regimens for those currently serving, according to U.S. officials...