Well Usain Bolt reached a top speed of 12.27 meters per second. You might think he doesn't even need to jump. Just run fast enough across the surface and he would escape from Deimos.
And - any sprinter able to compete in the modern Olympics final can manage an average of not much less than 10 meters per second over 100 meters. But you don't even need that. 6 meters per second isn't hard for a sprinter to achieve, apparently.
But without gravity it's likely to be harder.
High jumpers can leave the ground at 4.2 meters per second with a run up. High Jump Run-Up - nearly enough. And you might think you could leave the ground more quickly in low gravity.
But you wouldn't get much of a run up in the low Deimos gravity. Especially in a spacesuit. You'd leave the ground first. And a standing jump would be even harder.
And running across the surface also has the problem that after a few strides, you end up lifting off the ground and entering into orbit around Deimos, so you can no longer touch the ground to keep running.
So, I suspect the answer is probably, no. But don't know if anyone has gone into this in detail.
Now, if you were to build a quarter circle ramp, starting off horizontally and then ramping up vertically, that would be different. Run along it quickly enough and you'd build up to full g of artificial gravity, could sprint like a sprinter, and sprint into space.
You'd probably build a full circle one, and next to it, a quarter circle one. So you run around the full circle one a couple of times building up speed (going upside down in the process which would be easy in the weak gravity), then last time, you run onto the quarter circle one and sprint into space.
We can also work out its size. If you need 1 g for sufficient traction and can run at 10 meters per second - Olympics class sprinter - then you could make it 10 meters in radius. If you can do with 0.1g and still achieve 10 meters per second you can make it a much larger 100 meters in radius.
If you can only manage 6 meters per second, then you can make it 37 meters diameter for 0.1 g or 3.7 meters in diameter if you need 1 g for traction.
With one of those I'd imagine most healthy humans could sprint to escape velocity from Deimos. Or, indeed from some of the smaller asteroids also, similarly sized ones. Assuming very flexible spacesuits, not our present generation ones. Hard to imagine anyone sprinting in those.
I don't recommend anyone does this :). Well not with present day technology, easily get lost in space with no hope of rescue. It's just a fun calculation.
BTW just found an XKCD graphic which suggests the idea of using a bike and a ramp, you could do that too, rather similar idea. ... Page on xkcd.com
Deimos has many craters so maybe one of those could help for use as a ramp or to help with building our circular track for building up speed. (nice idea in the comments by Kasper Emil Feld :) )