This depends on how much mass the Sun is losing and at what stage it is in its life cycle.
The Sun currently loses approximately 170 trillion tonnes of mass each year, primarily through nuclear fusion (about 126 trillion tonnes) and the solar wind (about 47 trillion tonnes).
At first glance, 170 trillion tonnes sounds like an enormous amount of material. However, the Sun is so vast that this annual loss represents only about 0.0000000085% of its total mass.
This loss of mass does have an effect on Earth. As the Sun loses mass, its gravitational attraction weakens slightly, causing Earth's orbit to gradually expand. The effect is extremely small and virtually unnoticeable on human timescales.
Currently, Earth moves away from the Sun by approximately 1.5 centimetres per year. At that rate, after one million years, Earth would be only about 15 kilometres farther from the Sun than it is today.
When the Sun enters its Red Giant phase, mass loss will increase dramatically. As a result, Earth's outward migration will occur more rapidly. Even then, the change will still be very difficult to detect on human timescales.
During the Red Giant phase, the Sun is estimated to lose between 1 and 10 quintillion tonnes of mass per year. This increased mass loss is expected to accelerate Earth's outward movement to tens of kilometres per year, with rates potentially reaching hundreds of kilometres per year during periods of intense mass loss in the late Asymptotic Giant Branch (AGB) phase. This occurs during the final few million years before the Sun sheds its outer layers as a planetary nebula and becomes a white dwarf.
Over this entire evolutionary process, Earth's orbit is expected to expand from its current distance of approximately 150 million kilometres from the Sun to around 270 million kilometres. This increase would occur solely as a result of the Sun losing nearly half of its mass over the next 5 billion years or more.
In summary, while the Sun's loss of mass does cause Earth to gradually move farther away, the effect is incredibly small today. The most significant orbital expansion will occur during the Sun's final stages of evolution, billions of years from now, when mass loss rates become vastly greater than they are at present