More than "likely"
It's a thermodynamic-odds certainty that we can't find any dead alien probes that are drifting in the solar system. We can just about notice rocks tens of meters across ... if they happen to come close enough to Earth's orbit to attract out attention.
An alien interstellar probe is unlikely to be bigger than a coke can. (I'm assuming a modicum of technological advancement, but no way to beat the speed of light.) It might once have had a solar sail, but if it hadn't evaporated within a few years of its deployment, those aliens were wasting an awful lot of energy sending it here!
I haven't had enough coffee to think about the physical limits on detectability, but there are such. Radar is probably the best bet. How far away does a coke can have toi be, before its radar reflection becomes undetectable in the universal background noise? I'd hazard a guess, inside the orbit of Mars. Tht leaves a LOT of solar system outside. Anyway, the solar system is chock-full of coke-can-sized rocks to detect. How to spot the needle in the haystack?
BTW alien probes that landed on Earth will long ago have been destroyed by geological or biological activity. Or if neither of those, just undetectably buried in kilometers of solid rock. (I'll ignore the extra energy budget needed to send something that could land on a planet across interstellar distances!) Best hope for aliens that really, really wanted to leave a probe where the developing life on earth would find it many millions of years in their future, would be the moon. But even there, it would get covered in dust.
An active probe, sent across interstellar space to carry on bleeping at probably non-existent locals rather than devoting all its energy budget to communicating back with its makers? Seems unlikely. That it can stay "live" for as small a span of time as a million years? Improbable squared, and we've probably still missed it by more millions of years.
About the only thing we can rule out is hegemonising swarms of Von Neumann robots. The Fermi paradox definitely does apply to them; they aren't here so they don't exist in this galaxy.