Clustering assigns data points into groups called clusters, which define the characteristics of similar data points. Our work defines a model to identify and assess the presence of a clusterable structure initially in a two-dimensional density grid of a data set which is respectively expanded into a multidimensional density grid according the dimensionality of the data set. Clusterability is defined as the tendency of a data set having a structure for successful clustering. Our approach consists of a multimodal, convolutional neural network to assess the clusterability of a data set. Multimodality is the utilization of multiple sources of information. The output of our approach, the created model, also identifies the type of the clusterable structure (none, centroid and density). Our approach does not require an initial clustering of the data to define its clusterability. In the assessment of the clusterability of high-dimensional data, we utilize random rotations accompanied with an ensemble approach. The multiple experiments of various clustering problems illustrate that our proposed approach is capable of assessing the clusterability of data and of identifying the type of the clusterable structure.