The significance would depend upon how distant "distant" is. It also depends upon what you mean by moving toward us.

The more distant the galaxy, the larger its redshift will be. In the BB Theory this is interpreted as resulting from expansion of the universe and therefore the interpretation is that the galaxy is moving away from the Milky Way. Taking the Hubble Constant to be 70 km s-1 Mpc-1 we can say that a galaxy at a distance of 100 Mpc should have a redshift velocity of 7000 km s-1 - or be moving away with a velocity of 7000 km s-1.

However, galaxies can have peculiar motions due to orbital motions in clusters from gravitational interactions. If a galaxy is approaching us in its orbit with an orbital velocity of 1000 km s-1 (even as it recedes overall with the expansion of the universe), its redshift velocity will be 6000 km s-1. If this is what you mean by approaching, then there is nothing unusual.

Now if you mean the galaxy is blueshifted instead of redshifted, then its distance becomes important. The most distant galaxies with blueshifts are in the Virgo cluster. For example, NGC 4569 in Virgo has a redshift velocity of (minus) -137 km s-1. Depending upon its exact distance (12-17 Mpc) it has a peculiar motion of about -1000 km s-1 to -1500 km s-1. This is considered acceptable as a peculiar motion and does not necessarily indicate anything unusual.

However, if you had a galaxy at 100 Mpc with a measured blueshift, then that would be highly problematic because its peculiar motion toward the Milky Way would be greater than -7000 km s-1. In other words it would be moving against the Hubble flow at that speed. It is generally acknowledged that peculiar motions should not exceed 1500 km s-1.