The west African country's leading player, Emmanuel Adebayor, said this week he would boycott next month's tournament in South Africa because of a dispute with the Togolese Football Federation (TFF) over claims of unpaid money.
Six said in an interview with Radio France International that his position was becoming untenable because of the row.
"I'm held hostage by the situation and I have no other solution but to think about my future," said the former French international.
"This raises inevitable questions about a year spent putting a team together and then the entire edifice crumbling inside a very short time."
Six said he was now contacting other leading players in the squad to check on their commitment to the Jan. 19-Feb.10 tournament. Togo have been drawn in a difficult pool along with favourites Ivory Coast and past winners Algeria and Tunisia.
"I'm not the type to abandon the ship if things go wrong but I'm not the one to try and keep the balance either," the coach added.
Togo's players accuse their federation of reneging on promises over payments, an on-going affair that has continually dogged Adebayor's relationship with his country's national team since the 2006 World Cup when money issues overshadowed the team's appearance at the finals.
"We believed the problems would be solved and we would prepare for the Nations Cup in a good atmosphere," added goalkeeper Kossi Agassa of Ligue 1 club Stade de Reims, also interviewed by Radio France International.
"But if the coach goes and Adebayor is not there, then you can expect others will also pull out."