"If the Prime Minister Brexit's agreement can not lead to MPs backing Parliament, the alternatives must be decided," Liam Fox said ,
The Cabinet Brexiteer said that if there was no change in the backstop issue, "it is unlikely that it will happen to parliament".
He said that another referendum was unlikely, but did not rule out that MPs would get a "free vote" in different ways.
Theresa May has accused former Labor Prime Minister Tony Blair of undermining the Brexit talks by calling for another referendum.
She met EU leaders on Thursday after postponing a lower house vote on the withdrawal agreement she had negotiated with the EU for fear of her severe defeat The House of Commons will continue in January as talks with the EU on the issue of the Irish border continue "backstop".
The backstop is an "insurance policy" in the retreat agreement designed to prevent the return of a hard border with Northern Ireland if no trade agreement is reached ̵
1; however, many Ms May's deputies say they can not support this on the grounds that Britain would remain bound by EU rules indefinitely and limit its ability to reach trade agreements Deal is "not open for renegotiation" – but there could be further clarification.  International Trade Secretary Fox told Andrew Marr's BBC One show that discussions with Brussels over Christmas and the New Year would continue on how the backstop could be operable "mutually acceptable".
"If the MEPs' fears are not reflected and they may be blocked regardless of the attack, they are unlikely to pass through Parliament."