Officers say 33-year-old Mamun Ahmed may be able to help with the investigation into the incident in the St George's Quay area of the city in the early hours of last Thursday.
They say the incident happened around 3:10am. A man was disturbed and ran off towards the flood defences on the quayside and then onto Carlisle Bridge.
A police spokesperson said that following further enquiries detectives would like to speak to Ahmed, 33, as part of their investigation.
He is described as 5ft 6in tall and is of Bangladeshi nationality.
DS Chris Hammond, of Lancaster CID, said: "This was a shocking and very worrying incident which has left the victim very shaken and upset.
"We realise this will have caused a lot of concern in the community and following further enquiries we now want to speak to Ahmed in connection with the offence.
"If you know where Ahmed is, or have any information about his whereabouts, please come forward.
"I would also encourage Ahmed to come forward and contact police immediately."
Anyone with information is asked to email [email protected] or call 101, quoting log 0157 of October 21, 2021.