TL;DR: gRPC Python on Linux will transition from manylinux1 to manylinux2010 in early 2020. If you use a pip version earlier than 19, please upgrade it to 19 or higher to continue downloading binary packages rather than from-source packages.
gRPC Python currently distributes manylinux1 binary wheels on Linux to provide binary wheels for various Linux distributions compliant with manylinux1 (PEP-513). Since manylinux1 is superseded by manylinux2010 (PEP-571), gRPC Python will transition from manylinux1 to manylinux2010 from 2020. Since gRPC 1.24.3, gRPC Python has been distributed for both manylinux1 and manylinux2010 and ~80% pip downloads are for manylinux2010, ~14% are for manylinux1, and others are for source wheels. Most of the manylinux1 downloads are not because of the OS capability but because of the lower PIP version.
manylinux2010 will provide several benefits. It can have better performance due to modern build tool chain and recent OS features introduced by manylinux2010 mandating glibc 2.12 or higher.
Once the transition happens, if the version of pip is lower than 19, it might result in downloading a source package and building it from source instead of downloading pre-built package. This would be far slower than installation with binary wheels and it may fail due to lack of required build tools.
Since manylinux2010 is based on CentOS 6, with Linux system which doesn’t have glibc 2.12 or higher and libstdc++ 6.0.13 or higher (notably CentOS 5), gRPC Python won’t work. Please consider upgrading OS or use gRPC 1.26, the last version distributed with a binary wheel for manylinux1.