Relying on the powerful communication capabilities and rapidly changing geometric configuration, the Low Earth Orbit (LEO) satellites have the potential to offer integrated communication and navigation (ICAN) services. However, the isolated resource utilization in the traditional satellite communication and navigation systems has led to a compromised system performance. Against this backdrop, this paper formulates a joint beamforming design and satellite selection optimization problem for the LEO-ICAN network to maximize the sum rate, while simultaneously reconciling the positioning performance. A two-layer algorithm is proposed, where the beamforming design in the inner layer is solved by the difference-of-convex programming method to maximize the sum rate, and the satellite selection in the outer layer is modeled as a coalition formation game to simultaneously reconcile the positioning performance. Simulation results verify the superiority of our proposed algorithms by increasing the sum rate by 16.6% and 29.3% compared with the conventional beamforming and satellite selection schemes, respectively.