The history of magnetism in Western Europe, as distinct from that of the compass, is fairly confused. One modern book on medieval technology states that "both European and Chinese antiquity were aware of the ability of the lodestone (a variety of magnetite) to attract and repel iron...", but no source for this is given. [Gies & Gies 1995 p 93] Indeed, the statement itself as it stands is incorrect as a lodestone will only attract (and not repel) unmagnetized iron. Nevertheless, the statement is not implausible.
The first actual mention of magnets (again as opposed to the compass) seems to be a reference to them in the Roman d'Enéas, composed between 1155 and 1160, in which it is written that the walls of Dido's Carthage were studded with magnets so that an armed man, approaching too closely, would be pulled to the wall and held tightly. (I am indebted to Prof. Kathryn Talarico for bringing this reference to my attention.) From the text it is clear that this attractive property of magnets was well-known to its readers, since no explanation of this property of is offered. On the other hand, the story occurs during a recitation of the wonders of Carthage; clearly the reader or auditor of the Enéas is being invited to marvel.
The next written work in the West mentioning magnetism (as opposed to discussing the compass) seems to have been the De universeo creaturarum written by William of Auvergne in 1231-6 when he was Bishop of Paris. He explained the motion of the celestial spheres by analogy to magnetic induction, the ability of a magnet to magetize a piece of iron. [White 1962 p 132]
Jean Gimpel notes that Petrus Peregrinus (Peter of Maricourt), who was considered by Roger Bacon to be the foremost experimentalist of his day, in 1269 wrote Epistolae de Magnete (Letters on the Magnet) to a Picard countryman, Suggerius of Foncaucourt. In this Peter explained the "laws" by which magnets repel and attract each other and how to identify the poles of a compass. Gimpel notes that Peter's work was so complete that no further studies on the properties of magnets were done until the monumental work of William Gilbert in 1600 (in which he included extracts from the work of Peter of Maricourt). [Gimpel 1976 p 193ff]
The compass was known in Europe in the late 12th century, so that it is essentially certain that the properties of magnets were known to some in Western Europe by that time. This agrees with the literary evidence given above. And it is clear that the properties of magnets had been decently explored a century later. More than this cannot be said.