New Horizons clocked in at about 37,000 mph, but Voyager 1 reached 38,350 mph leaving our solar system. These two are cited as the fastest of all our space probes. This is especially odd since they both achieved this feat going the opposite direction of our sun. One would expect that the fastest probe speed would be achieved by one of the crafts that explored Mercury, since they would have the additional benefit of increased speed as they accelerated towards the sun.
38,350 is impressive, but it is no where near the 112,000 to keep up with Mercury. To orbit Mercury, a probe would be required to be moving the same speed as the planet, and at the same exact time be accelerating against the gravitational pull of our sun to avoid getting sucked in.