The Premier League new boys agreed deals to sign Halliche on loan and French midfielder Situ on transfer deadline day.
However, Swansea have yet to find out if Fifa have officially sanctioned the deals leaving both players in limbo.
Swansea have not given up hope that the pair could still be available to make their debuts against West Brom this weekend but chairman Huw Jenkins revealed he is growing increasingly frustrated at the situation.
"We are hoping to get some information on the two signings very soon," Jenkins told the South Wales Evening Post.
"This situation is not ideal, and we just want to know one way or the other now.
"This is an issue that we've been discussing for a long time - the fact that in some cases, like the Fulham transfer, we get discriminated against.
"When we are trying to complete deals for players, we have to go through additional processes that other clubs in our league do not because any transfer between England and Wales is viewed as an international transfer."