said the alarm was raised not long after 8am.
In the hours that followed a search was carried out and soon after 11am one man was airlifted from the water and taken to hospital.
A statement said: “HM Coastguard coordinated the response to a report of a missing man from a passenger vessel off Liverpool.
"The alarm was raised at about 8.15am on 20 January and a search carried out.
“The HM Coastguard helicopter from Caernarfon was sent as well as RNLI all-weather lifeboats from Hoylake, Rhyl, Lytham St Annes and Llandudno.
"A man was airlifted from the water by the HM Coastguard helicopter at about 11.20am, transferred to an ambulance and taken to hospital.
“Crosby Coastguard Rescue Team assisted by securing a helicopter landing site. Merseyside Police were informed.”
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Stena Line said services were running as normal.
In July last year a man died after falling overboard from a Stena Line ferry near the port of Cairnryan in southern Scotland.
The ferry had been sailing to Belfast in the afternoon.
Rescue crews were called to the Stena Superfast VIII at Loch Ryan in Dumfries and Galloway shortly before 6pm.
The passenger was airlifted to hospital where he was pronounced dead. Police Scotland said the death was not believed to be suspicious.
Stena Line said the ferry's own rescue boat had been launched to recover the passenger from the water.
An HM Coastguard helicopter then airlifted the man from the vessel to University Hospital in Ayr.