Condor is hoping to start high-speed passenger sailings again from Friday 21 May.
That is only if travel and quarantine restrictions in the UK, France, and Channel Islands are relaxed by then.
This news follows the roadmap to recovery announcement from Boris Johnson, which included the hope that international travel could resume from 17 May at the earliest.
"We are absolutely committed to a resumption in passenger services and the recent surge in interest following the British government’s announcement last week has given us cause for optimism.
"Any restart does, though, require an agreement on border opening and currently there is no certainty when any easing of such controls will be possible." - Elwyn Dop, Condor's Operations Director.
A Jersey roadmap, including news on plans to ease Jersey's border restrictions, is due to be unveiled before the end of this week.
The Commodore Clipper will carry on running daily trips between the Channel Islands and Portsmouth, as well as the fortnightly round trips to St Malo.
Condor says it will contact passengers planned to travel with them before 21 May.

Guernsey to get serious about film industry expansion
JT Group acquires Isle of Man's leading telecoms provider
First brick laid at Guernsey's upcoming Wildlife Hospital
Farming in Herm dates back six millenia
Guernsey's water storage increases by 1% in 24 hours
Guernsey primary school gets daily vegetable tasters
Storm Benjamin dramatically ends Guernsey's dry spell
Tireless Guernsey fundraiser "re-energised" by awards evening