No. Avid qualifies Pro Tools on specific Windows and macOS versions only, and there is no Linux build. Ardour and REAPER are the serious Linux replacements, and REAPER even reads some of your work.
Pro Tools by Avid · Music & audio · No way to run it
Avid's compatibility documentation for Pro Tools is a list of tested and qualified Windows and macOS
versions. Linux does not appear, there is no unsupported-but-working build, and Avid's support only
covers the configurations on that list.
This is a real loss if you work with other studios, because Pro Tools session files are the exchange
format in professional audio. Nothing on Linux opens a .ptx session with plug-ins and automation
intact. If you send sessions to a mix engineer, keep a Windows or Mac machine for that.
For your own work, the ground is better than people expect. REAPER has an official Linux build and
an unusually generous licence, and it behaves much like Pro Tools once you set up the key bindings.
Ardour is free, open source, and built around recording and mixing rather than loops, which is close
to how Pro Tools thinks.
Move your projects as stems. Export each track from Pro Tools as a WAV file starting at the same
point in the timeline, and any Linux program can rebuild the session from those. Plug-ins are the
other catch: Windows VST plug-ins do not simply run on Linux, and AAX plug-ins run nowhere else at
all, so expect to replace them.
Official Linux version, small download, and a licence that costs far less than a Pro Tools subscription. Heavily customisable, which is how people make it feel familiar.
Your files: Cannot open .ptx sessions. Imports WAV stems and AAF exchange files from Pro Tools.
Only if you used Pro Tools for simple two-track recording and tidying rather than multitrack production.
Your files: Opens WAV, AIFF, FLAC and MP3 files.
This doesn't have to stop you
One stubborn program doesn't have to decide the whole question. You can keep Windows on the same PC and restart into it only when you need Pro Tools. Everything else you do can move.