The PM hits back at criticism from Tory MPs that post-lockdown restrictions are not properly targeted.
The company could make an announcement as soon as Monday, putting 13,000 jobs at risk.
Bowling alleys and indoor entertainment venues will also have to close under new restrictions.
The referral is "a significant first step" to a possible rollout of the vaccine, the government says.
It has been suggested that all schools could close on 18 December and reopen on 11 January.