The Cottagers are concerned about the ability of their safety staff to travel to Wednesday's match as a result of strike action affecting the London Underground
Tube workers have planned a 48-hour walkout for 21.00GMT on Tuesday, reportedly throwing some midweek games in the capital into doubt.
The Londoners are concerned about the ability of their safety staff to get to Craven Cottage, with a further announcement set to be made on Tuesday.
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"However, the club has concerns over the potential impact that the strike may have on the ability of its safety staff to attend the ground in sufficient time and numbers to ensure that it is able to open the ground and effectively operate it, from the time that the gates are open to the public until the departure of all supporters.
"After consulting with the Local Authority and the Metropolitan Police, it has been decided that, if the proposed action is still undetermined at 15.00GMT [on Tuesday] and the club cannot guarantee enough staff are available to attend the ground in sufficient time and numbers, then as a consequence the club would not be able to comply with the terms of its safety certificate and the fixture would be postponed and rescheduled for a future date.
"A further statement will be released at 15.00GMT [on Tuesday] to confirm whether the game will go ahead or be postponed."
A spokesperson for Liverpool added: "We will inform supporters through our official channels as soon as more information becomes available regarding the fixture.
"The safety and well-being of supporters has to be the paramount concern of everyone involved in this process."