Recommender systems are widely applied in digital platforms such as news websites to personalize services based on user preferences. In news websites most of users are anonymous and the only available data is sequences of items in anonymous sessions. Due to this, typical collaborative filtering methods, which are highly applied in many applications, are not effective in news recommendations. In this context, session-based recommenders are able to recommend next items given the sequence of previous items in the active session. Neighborhood-based session-based recommenders has been shown to be highly effective compared to more sophisticated approaches. In this study we propose scenarios to make these session-based recommender systems diversity-aware and to address the filter bubble phenomenon. The filter bubble phenomenon is a common concern in news recommendation systems and it occurs when the system narrows the information and deprives users of diverse information. The results of applying the proposed scenarios show that these diversification scenarios improve the diversity measures in these session-based recommender systems based on four news datasets.