Prepare environment

docker run -i -t --rm -v ${PWD}:/mnt \
  -e PIP_BREAK_SYSTEM_PACKAGES=1 \
  -e PIP_ROOT_USER_ACTION=ignore \
  -e PIP_NO_WARN_SCRIPT_LOCATION=0 \
  --name=buildenv alpine:latest \
    sh -c 'apk add bash; bash'

Install build tools:

apk update
apk add build-base
apk add curl
apk add gcc g++ gawk autoconf automake libtool
apk add pkgconf m4 gettext gettext-static gettext-dev
apk add cmake
apk add py3-pip
apk add acl-dev
apk add attr-dev
apk add xxhash-dev
apk add zstd-dev
apk add lz4-dev
apk add openssl-dev
python3 -m pip install --user commonmark
apk add musl-dev
apk add popt-dev
apk add zlib-dev
apk add openssl-libs-static

Create work directory:

mkdir /work
cd /work

Prepare zstd library:

curl -fsSLO https://github.com/facebook/zstd/releases/download/v1.5.7/zstd-1.5.7.tar.gz
tar -zxf zstd-1.5.7.tar.gz
cd zstd-1.5.7
make PREFIX=/opt/zstd install
cd ..

Export zstd variables:

export LDFLAGS="-L/opt/zstd/lib${LDFLAGS:+ $LDFLAGS}"
export CPPFLAGS="-I/opt/zstd/include${CPPFLAGS:+ $CPPFLAGS}"
export PKG_CONFIG_PATH="/opt/zstd/lib/pkgconfig${PKG_CONFIG_PATH:+:$PKG_CONFIG_PATH}"
pkg-config --cflags --libs --static libzstd

Prepare lz4 library:

curl -fsSLO https://github.com/lz4/lz4/releases/download/v1.10.0/lz4-1.10.0.tar.gz
tar -zxf lz4-1.10.0.tar.gz
cd lz4-1.10.0
make PREFIX=/opt/lz4 install
cd ..

Export lz4 variables:

export LDFLAGS="-L/opt/lz4/lib${LDFLAGS:+ $LDFLAGS}"
export CPPFLAGS="-I/opt/lz4/include${CPPFLAGS:+ $CPPFLAGS}"
export PKG_CONFIG_PATH="/opt/lz4/lib/pkgconfig${PKG_CONFIG_PATH:+:$PKG_CONFIG_PATH}"
pkg-config --cflags --libs --static liblz4

Prepare popt library:

curl -fsSLO https://github.com/rpm-software-management/popt/archive/refs/tags/popt-1.19-release.tar.gz
tar -zxf popt-1.19-release.tar.gz
cd popt-popt-1.19-release
./autogen.sh
./configure --prefix=/opt/popt
make install
cd ..

Or from master with the static lib patch:

curl -fsSL https://github.com/rpm-software-management/popt/archive/refs/heads/master.zip -o popt-master.zip
unzip -q popt-master.zip
cd popt-master
curl -fsL https://github.com/rpm-software-management/popt/pull/104.diff | patch -p1
cmake -S . -B ./build -DBUILD_STATIC_LIBS=ON -DCMAKE_INSTALL_PREFIX=/opt/popt
cd build
make install
cd ../..

Export popt variables:

export LDFLAGS="-L/opt/popt/lib${LDFLAGS:+ $LDFLAGS}"
export CPPFLAGS="-I/opt/popt/include${CPPFLAGS:+ $CPPFLAGS}"
export PKG_CONFIG_PATH="/opt/popt/lib/pkgconfig${PKG_CONFIG_PATH:+:$PKG_CONFIG_PATH}"
pkg-config --cflags --libs --static popt

Prepare attr library:

curl -fsSLO https://download.savannah.nongnu.org/releases/attr/attr-2.5.2.tar.xz
tar -xf attr-2.5.2.tar.xz
cd attr-2.5.2
sed -i '/#include <stdlib.h>/a #include <libgen.h>' tools/attr.c
./configure --prefix=/opt/attr
make install
cd ..

Export attr variables:

export LDFLAGS="-L/opt/attr/lib${LDFLAGS:+ $LDFLAGS}"
export CPPFLAGS="-I/opt/attr/include${CPPFLAGS:+ $CPPFLAGS}"
export PKG_CONFIG_PATH="/opt/attr/lib/pkgconfig${PKG_CONFIG_PATH:+:$PKG_CONFIG_PATH}"
pkg-config --cflags --libs --static libattr

Prepare acl library:

curl -fsSLO https://download.savannah.nongnu.org/releases/acl/acl-2.3.2.tar.xz
tar -xf acl-2.3.2.tar.xz
cd acl-2.3.2
./configure --prefix=/opt/acl
make install
cd ..

export LDFLAGS="-L/opt/acl/lib${LDFLAGS:+ $LDFLAGS}"
export CPPFLAGS="-I/opt/acl/include${CPPFLAGS:+ $CPPFLAGS}"
export PKG_CONFIG_PATH="/opt/acl/lib/pkgconfig${PKG_CONFIG_PATH:+:$PKG_CONFIG_PATH}"
pkg-config --cflags --libs --static libacl

Prepare xxHash library:

curl -fsSL https://github.com/Cyan4973/xxHash/archive/v0.8.3.tar.gz -o libxxhash-0.8.3.tar.gz
tar -zxf libxxhash-0.8.3.tar.gz
cd xxHash-0.8.3
make PREFIX=/opt/xxhash install
cd ..

Export xxHash variables:

export LDFLAGS="-L/opt/xxhash/lib${LDFLAGS:+ $LDFLAGS}"
export CPPFLAGS="-I/opt/xxhash/include${CPPFLAGS:+ $CPPFLAGS}"
export PKG_CONFIG_PATH="/opt/xxhash/lib/pkgconfig${PKG_CONFIG_PATH:+:$PKG_CONFIG_PATH}"
pkg-config --cflags --libs --static libxxhash

Download rsync source code:

curl -fsSLO https://rsync.samba.org/ftp/rsync/src/rsync-3.4.1.tar.gz
tar -zxf rsync-3.4.1.tar.gz
cd rsync-3.4.1

Check https://rsync.samba.org/ftp/rsync/src/ for latest available version

Prepare build configuration:

./configure

As a result, you should see rsync 3.4.1 configuration successful message.

Compile:

make CFLAGS="-static" EXEEXT="-static"
strip rsync-static
cp rsync-static /mnt
exit

$ file rsync-static
rsync-static: ELF 64-bit LSB executable, x86-64, version 1 (SYSV), statically linked, BuildID[sha1]=fde6468edf61242954e2dae866a6b63324178136, stripped