Multi-processors System-on-Chip (MPSoC) are a key enabling technology for different applications characterized by hyper-connectivity and multi-tenant requirements, where resources are shared and communication is ubiquitous. In such an environment, security plays a major role. To cope with these security needs, MPSoCs usually integrate cryptographic functionalities deployed as software and/or hardware solutions. Quantum computing represents a threat for the current cryptography. To overcome such a threat, Post-quantum cryptography (PQC) can be used, thus ensuring the long term security of different applications. Since 2017, NIST is running a PQC standardization process. While the focus has been the security analysis of the different PQC candidates and the software implementation, the MPSoC PQC implementation has been neglected. To this end, this work presents two contributions. First, the exploration of the multicore capabilities for developing optimized PQC implementations. As a use case, NTRU lattice-based PQC, finalist for the NIST standardization process, is discussed. Second, NTRU was deployed on an AURIX microcontroller of Infineon Technologies AG with the Real-Time Operating System PXROS-HR from HighTec EDV-Systeme GmbH. Results show that NTRU can be efficiently implemented and optimized on a multicore architecture, improving the performance up to 43% when compared to single core solutions.