This paper presents a novel exploration of Fully Homomorphic Encryption (FHE) applied to the problem of Maximal Extractable Value (MEV) in blockchain transactions, explicitly focusing on arbitrage scenarios. Building upon previous work by Flashbots, we adapt their secret-sharing-based protocol to FHE to reduce data transmission overhead. We introduce a protocol that enables searchers to blindly backrun a user transaction, executing specific conditions and arithmetic operations on the transaction content using FHE. Our protocol leverages the TFHE scheme to handle the data extraction, constraint verification and arithmetic calculation on 128-bit unsigned integers representing the tokens stored on the UniswapV2 Decentralised Exchange (DEX). Despite significant runtime constraints, our work provides a solid foundation for future research, identifying key areas for improvement and expansion. This study represents a significant advancement in applying FHE to blockchain transactions, stimulating further collaboration within the FHE community to address open challenges and bring privacy-preserving protocols for MEV mitigation closer to real-world deployment.