Although there is no jurisdictional bar to general federal jurisdiction over an initial denial of asylum, the administrative record has not yet been sufficiently developed by the exhaustion of administrative remedies that would result from challenging a subsequent enforcement of the decision, so jurisdiction is not yet proper under the APA.
http://media.ca7.uscourts.gov/cgi-bin/rssExec.pl?Submit=Display&Path=Y2018/D07-13/C:17-3377:J:Ripple:aut:T:fnOp:N:2185998:S:0
Since 2011. An occasional commonplacing of the U.S. Circuit Courts of Appeal.
Neither an authoritative statement of the law nor legal advice. Quick work.