I tried both 1.8.3 and 1.8.4 with the same result:

2 issues are described

a) The configuration process successfully completes: ./configure --enable-proxy --enable-static --with-sqlite3
but then the last step of the make process returns: "/usr/bin/ld: cannot find -lsqlite3" because libsqlite3.a isn't included in either the sqlite or the sqlite-devel package (i think Configure should check and complain), so it's needed to manually compile sqlite from sources and point the configure to the new path.

b) But even after that, the make process still fails with various undefined reference errors related to sqlite library (i.e.: /root/zabbix-1.8.3/src/libs/zbxdb/db.c:757: undefined reference to `sqlite3_free_table').
In order to fix this I had to manually edit the src/zabbix_proxy/Makefile and change:

LIBS = -lm -lresolv
to
LIBS = -lm -lresolv -lsqlite3 -ldl -lpthread

after that, the make process finished successfully