South Africa midfielder Furman earned a place in the host nation's squad for the tournament that begins on January 19.
FIFA rules dictate players must be made available to their countries two weeks prior to the start of major international tournaments, with any earlier release at the discretion of the clubs involved.
Latics manager Paul Dickov has used this to his advantage and, against the wishes of the South African FA, Furman will turn out in his side's third-round FA Cup clash at Nottingham Forest before hot-footing it to Heathrow.
"They (South African FA) are not overly pleased about it but it was up to the club whether they let me go early or not and they want me here for the game, so I'm here for the game and all my thoughts are on it," said Furman.
"I leave straight away after the game. I've got a nine o'clock flight from London so I don't know how I'm going to get there in time but I'm pretty focused on the game - I can worry about that after.
"It's really, when the final whistle blows, a sprint to the shower if I've got any energy left and get in the taxi straight away down to Heathrow."
And Furman hopes to take his seat in the departure lounge buoyed by a famous victory at odds with the stuttering league former that has seen Oldham slump to 19th in npower League Two and cost three members of Dickov's backroom staff their jobs last week.
"It's a welcome respite from the league where our form over the last month hasn't been good at all," the 24-year-old added.
"No one expects us to win. We can go there without any pressure and want to give a really good account of ourselves, play the free-flowing football that we can do and we want to win the game. We want to progress to the fourth round."