Taylor's ankle sprain has ruled him out for four weeks while Orlandi will be out for two weeks with a thigh strain.
Third-choice Jazz Richards is to retain his left-back spot for Saturday's third round game as Taylor is out and regular left-back Alan Tate is still banned.
Welsh international Taylor has made 15 Championship appearances for the Swans since signing from Welsh rivals Wrexham in the summer.
Spaniard Orlandi has been a regular for the Championship play-off chasers but Swans boss Brendan Rodgers has plenty of midfield cover with Joe Allen, Darren Pratley, Mark Gower and Kemy Agustien all fit.
Former Wales under-21 international Shaun MacDonald has also returned to the Liberty Stadium after his four-month loan spell at League One Yeovil Town - and is another midfield option for Rodgers.
Young striker Kerry Morgan has also returned from his loan spell at Blue Square Bet Premier side Newport County.
Former Wales under-21 goalkeeper David Cornell, meanwhile, has been sent out to Welsh Premier side Port Talbot Town on loan for the rest of the season.
Source: BBC Sport
Source: BBC Sport