Show elapsed time every second running a bash script

I'm running a shell script in Linux Mint that calls some processes taking few minutes. For each process I want to echo a message like this:

echo "Cleaning temporary files... X seconds."
myprocess

where X is the current elapsed time and I would like it to change every second, but not printing a new line.

Is there a good way to do that? I only found ways to print the total time in the end, but not the elapsed time while running the process.