Trusted Platform Modules (TPMs) serve as the root of trust to design and implement secure systems. Conceived by the Trusted Computing Group, a computer industry consortium, components complying with the TPM 2.0 standard are stable and widely available. However, should large-scale quantum computing become a reality, the type of cryptographic primitives adopted in the current standard will no longer be secure. For this reason, this paper analyses the impact of adding three Post-Quantum (PQ) algorithms to a current non- Quantum Resistant TPM through software emulation. The experimental results give insight on the kind of implementation challenges hardware designers will face when integrating the new primitives onto the TPM, that typically features limited hardware resources and low power consumption. In particular, it is concluded that Kyber, NTTRU, and Dilithium can efficiently replace most of the functionality provided by Elliptic Curve Cryptography (ECC) and Rivest-Shamir-Adleman (RSA). In contrast, current PQ Direct Anonymous Attestation (DAA) protocols are currently not compact enough to fit into a hardware TPM.