The deadline-day arrivals were delayed by so-called minor issues, and consequently rejected by the sport's governors despite approval from the Premier League and FA
Despite the moves being backed by the Premier League, the FA, and others, the sport's governing body have blocked the deals for the two defenders due to minor delays in the processing of the transfers.
A statement from the club read: "Swansea City is disappointed with Fifa's decision and are currently pursuing other options to strengthen the squad.
"The club will not be making any other comment at this stage until full written clarification is received from Fifa."
The Welsh side may appeal the decision when they receive confirmation, having thought they had secured the £250,000 signing of Situ from Lens, and the loan of Halliche from Fulham.
In another defensive blow, Tottenham loanee Steven Caulker has had to return to his parent club for assessment of a knee injury.
19-year-old Caulker has started all four of the Swans’ Premier League games so far this season, but damaged his cartilage in a clearance in the 1-0 defeat by Arsenal last weekend.
The club said in a statement: “A scan this week confirmed the injury and Caulker will return to White Hart Lane tomorrow to be assessed further by club specialists when a further update will follow.”
Manager Brendan Rodgers, who returned to training on Thursday following the death of his father, must add the three players to his list of absentees ahead of Saturday’s fixture with West Brom.
Alan Tate is already out after breaking his leg in an accident with a golf buggy recently, midfielder Kemy Agustien suffered a hamstring problem against the Gunners, and captain Garry Monk is doubtful despite making speedy progress on his way back from a foot injury.
There is a boost, though, in the form of Wayne Routledge, who has returned to training having missed the Arsenal match with an ankle complaint.