Tesco is yet to decide on its position regarding employee Tom Stephens, who was suspended after being identified as a suspect in the investigation into the murders of five prostitutes in Ipswich.
Stephens, 37, was arrested in December on suspicion of being the 'Suffolk Strangler', but has since been released without charge.
Tesco has been warned by employment lawyers that it must be very careful when disciplining Stephens – especially now he has been cleared of the crimes.
A spokesman for the supermarket giant told Personnel Today: "An investigation is under way. We are looking into the conduct of the member of staff during this episode and will see what [action] is appropriate."
Emma Burrows, head of employment at law firm Trowers & Hamlins, said last month: "If Stephens is sacked, he could sue for wrongful dismissal. It would be a fascinating case."
Suffolk Police charged another local man, former QE2 steward Stephen Wright, 48, with the murders of Gemma Adams, Anneli Alderton, Tania Nicol, Paula Clennell and Annette Nicholls.