In the comics, the Speed Force does exist. DC comic speedsters generally derive their abilities from the Speed Force granting them speed, inter-dimensional travel, and time-travel (as well as a myriad of others). Characters like Barry Allen, Wally West, Bart Allen, Eobard Thawne, and Max Mercury all have connections to the Speed Force.
Superman, however, does not derive his speed from the Speed Force and therefore cannot time travel, no matter how fast he goes. Superman's abilities are extra-terrestrial and tied closely with the radiation from a yellow sun.
This disconnect is confirmed by the Marvel/DC crossover, JLA/Avengers. In the story, when the DC heroes arrive in the Marvel universe, The Flash loses his abilities because the Speed Force doesn't exist there. Superman's abilities are unaffected:
It's worth noting, though, that while Superman cannot time travel like The Flash can, the Silver Age Superman was able to travel through time when traveling at speeds faster than light; an ability that was retconned away decades ago. More info on that can be found here: Can Superman reverse time in comics by flying faster than speed of light?