We approach the problem of recognition and attribution of quotes in Finnish news media. Solving this task would create possibilities for large-scale analysis of media wrt. the presence and styles of presentation of different voices and opinions. We describe the annotation of a corpus of media texts, numbering around 1500 articles, with quote attribution and coreference information. Further, we compare two methods for automatic quote recognition: a rule-based one operating on dependency trees and a machine learning one built on top of the BERT language model. We conclude that BERT provides more promising results even with little training data, achieving 95% F-score on direct quote recognition and 84% for indirect quotes. Finally, we discuss open problems and further associated tasks, especially the necessity of resolving speaker mentions to entity references.