Digging source code shows following:
- Event loop is basically executing 
_run_once in while True loop 
_run_once does all stuff including waiting for a select to complete 
timeout to wait for select isn't stored anywhere outside _run_once 
Nothing stops us to reimplementing _run_once, so we can time what we need.
Instead of copying the whole _run_once implementation, we can time right before select, which is when _run_once started (because before select nothing time consuming happens) and time right after select is when _process_events started.
From words to action:
import asyncio
class MeasuredEventLoop(asyncio.SelectorEventLoop):
    def __init__(self, *args, **kwargs):
        super().__init__(*args, **kwargs)
        self._total_time = 0
        self._select_time = 0
        self._before_select = None
    # TOTAL TIME:
    def run_forever(self):
        started = self.time()
        try:
            super().run_forever()
        finally:
            finished = self.time()
            self._total_time = finished - started
    # SELECT TIME:
    def _run_once(self):
        self._before_select = self.time()
        super()._run_once()
    def _process_events(self, *args, **kwargs):
        after_select = self.time()
        self._select_time += after_select - self._before_select
        super()._process_events(*args, **kwargs)
    # REPORT:
    def close(self, *args, **kwargs):
        super().close(*args, **kwargs)
        select = self._select_time
        cpu = self._total_time - self._select_time
        total = self._total_time
        print(f'Waited for select: {select:.{3}f}')
        print(f'Did other stuff: {cpu:.{3}f}')
        print(f'Total time: {total:.{3}f}')
Let's test it:
import time
async def main():
    await asyncio.sleep(1)  # simulate I/O, will be handled by selectors
    time.sleep(0.01)        # CPU job, executed here, outside event loop
    await asyncio.sleep(1)
    time.sleep(0.01)
loop = MeasuredEventLoop()
asyncio.set_event_loop(loop)
try:
    loop.run_until_complete(main())
finally:
    loop.close()
Result:
Waited for select: 2.000
Did other stuff: 0.032
Total time: 2.032
Let's test it against code with real I/O:
import aiohttp
async def io_operation(delay):
    async with aiohttp.ClientSession() as session:
        async with session.get(f'http://httpbin.org/delay/{delay}') as resp:
            await resp.text()
async def main():
    await asyncio.gather(*[
        io_operation(delay=1),
        io_operation(delay=2),
        io_operation(delay=3),
    ])
Result:
Waited for select: 3.250
Did other stuff: 0.016
Total time: 3.266