The Magpies have lost nine of their last 11 matches and could probably do without a return to the scene of their fourth-round defeat in the same competition last season.
In-form striker Ba is also on the verge of joining Chelsea, but Poyet knows his side will still have to be at their best to pull off another giantkilling.
"It's not a great time for Newcastle in the league," the Uruguayan said.
"They played on Wednesday night so I'm sure there are plenty of things Alan Pardew will think about.
"That said, it's a cup competition live on TV so I wouldn't be surprised if they play their best team. They should be capable of beating us, they are a good team with great players.
"I'm very glad not to be facing Demba Ba, and if he wants to leave (Papiss) Cisse and company out I will be very happy as well.
"Maybe the fans want to see the best players at the Amex and he (Ba) is an outstanding player who can score from anywhere. It doesn't mean it will be easy, but I'm glad he's not there."
Poyet has long been a thorn in Newcastle's side in the FA Cup, having also scored twice against them for Chelsea in the 2000 semi-final before the Blues went on to lift the trophy.
"I don't know what my relationship with Newcastle is but it looks like I'm going to have it my whole career," he added.
"I think it's great and last year makes it even more interesting. It's another great game for me, our players and our supporters.
"We played Liverpool twice last year and now we play Newcastle again, it's the way the draw is. Me and Newcastle and the FA Cup, there is always a history there.
"I prefer to play Premier League teams and not Championship sides, so it's great for us. When you play against better teams you need to be very good and make it difficult for them as well as hoping for a bit of luck.
"This game is even more interesting because of last year. Newcastle will come here in a different way, they will make it even more difficult and it will be another great game of football for the supporters."