Not directly a tcpdump, but can give you info about the network traffic, check https://bytefreaks.net/gnulinux/how-to-capture-all-network-traffic-of-a-single-process
strace -f -e trace=network -s 10000 <PROCESS WITH ARGUMENTS>;
If the process is already started and you know its PID you can use the following
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strace -f -e trace=network -s 10000 -p <PID>;
Another alternative is more complex, using network namespaces, check the above link or use the tool nsntrace, but either can only work on new process, you can not change existent process network namespaces (AFAIK)
UPDATE:
you can also install the tool bpfcc-tools (search for your distro, many have it included already) and use the command sudo tcptracer-bpfcc -v -p (PID)
While this will not show the packets, it will list network connections for that pid. You can remove the -p (PID) to list all connections per process. This may be useful for those tracking short live connections, not the network payload.