Yes. Every object in this universe attracts another object as per the Newtons' law of gravitation. If there are two bodies (even as big as planets) with masses M1 kg and M2 kg and they are at distance of d from each other, There is always attraction only.
Gravitational Attraction force between them is = G M1 M2 / d²
There can be attraction between one body and another if they have magnetic property - north pole and south pole. But north pole and north pole of magnets repel each other.
There is an attractive force between positive electric charge and negative electric charge that is given by coulomb's law . If they have same sign , then they repel each other.
Moon is attracted to Earth, Earth is attracted to Sun and so on due to gravitational force.