An earlier decision to block residents from returning to the island has been criticised by those stuck in the UK and politicians.
However, Mr Quayle said the island’s Council of Ministers was following advice from clinicians.
It is now expected that Mr Quayle will make an announcement today, Monday April 6, about how residents will be able to return.
It appears likely that they will have to travel to Heysham and return to the island by boat.
Rumours were circulating last week that stranded Isle of Man residents had been camping at Heysham Port, waiting to be allowed home.
However, Peel Ports, who operate Heysham Port, said there are currently no campers on the site, and they are not aware of any having been there.
Mr Quayle said: “We have a plan, we are close to finalising the rigorous protocols that may allow the return of our residents in a managed, safe, staggered manner.”
Mr Quayle added that those trying to return to the island will not be able to just turn up at Heysham to book onto a boat; they will have to be invited.
Source`: Lancaster Guardian website