Can human push Earth away from the Sun?

The Earth is pretty heavy. No rocket that we can currently make is going to have much effect on it's motion.

The only remotely feasible suggestion I've seen is to divert asteroids from the asteroid belt so they pass close to the Earth in a slingshot orbit. The idea is to accelerate the asteroid and decelerate the Earth, which causes the Earth to move into a larger orbit. Any one asteroid isn't going to have a big effect, but there are a lot of asteroids out there so you would do it repeatedly.

There are potential problems of course. You still need a fair bit of energy to divert the asteroid, though you could do it with a solar sail if you had enough time. Also you'd need to be pretty sure you could divert the asteroid accurately as an error in the asteroids trajectory could prove embarrassing.

Anyhow, who told you the Earth is approaching the Sun? As far as I know it isn't, though because the Earth's orbit is an ellipse the Earth-Sun distance does decrease for for six months then increase again for the next six months.

There exist sun tides as well as moon tides. The moon is receding from the earth due to the tides , because of energy and angular momentum balances.

The same is happening very slowly to the distance of the orbit of the earth from the sun.

No, we are not approaching the sun, we are slowly distancing ourselves from it, as the moon is distancing from the earth.

There is an effect which is making us move very slowly away from the Sun. That is the tidal interaction between the Sun and the Earth. This slows down the rotation of the Sun, and pushes the Earth farther away from the Sun.

But how big of an effect is this? It turns out that the yearly increase in the distance between the Earth and the Sun from this effect is only about one micrometer (a millionth of a meter, or a ten thousandth of a centimeter). So this is a very tiny effect.

and it continues:

There is another effect which is also small, but somewhat bigger than the tidal effect. The Sun is powered by nuclear fusion, which means the Sun is continuously transforming a small part of its mass into energy. As the mass of the Sun goes down, our orbit gets proportionally bigger. However, over the entire main sequence lifetime of the Sun (about 10 billion years), the Sun will only lose about 0.1% of its mass, which means that the Earth should move out by just ~150,000 km (small compared to the total Earth-Sun distance of ~150,000,000 km). If we assume that the Sun's rate of nuclear fusion today is the same as the average rate over those 10 billion years (a bold assumption, but it should give us a rough idea of the answer), then we're moving away from the Sun at the rate of ~1.5 cm (less than an inch) a year

Why do you think that we need to push the Earth farther from the Sun? The rate at which the Earth is approaching the Sun in so minimal as to be inconsequential. The Sun will red giant before the Earth gets close enough to matter, and at that stage the increased distance will not help us.

In any case, to get farther from the Sun we would not push the Earth out from the direction of the Sun. Rather, at aphelion we would push the Earth in the direction of the Earth's travel around the Sun. If you are interested, you might want to read a bit about orbital mechanics.

Note also Anna's answer that the Earth may actually be receding from the Sun.