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
