The 24-year-old had to pull out of England's World Cup qualifiers against Moldova and Ukraine because of injury, but it appears likely he will play for Brendan Rodgers' men at the Liberty Stadium on Monday.
But, given the current discussions over the travails of the national side and the opportunities afforded to young players, Laudrup appeared sceptical when talking about Sturridge's recovery.
"I was a little surprised," he said. "We talk about a young player, a huge talent, and I am sure he would have played in a crucial game (for England) the other day.
"But he was injured and yet 48 hours later he is fit to play against us.
"I hope he plays as I want to play against Liverpool with their best players.
"But when we talk about England and young players and the importance of the game (in Ukraine), I was surprised to read less than 48 hours after such a crucial game that he is fit to play against us.
"I thought there were some rules that if you were injured you couldn't just play with your team three of four days later.
"But that's none of my business, I am just taking care of Swansea."
Sturridge, August's player of the month, has scored in Liverpool's first three Premier League games to help the Reds top the embryonic table.
Laudrup has been impressed by the way they have opened the campaign.
"They have had a great start, three games and nine points," he said.
"I like the way they play, you can see how they want to play and it was clear during the second half of last season.
"They are very good in possession and have brought in some very good players like Philippe Coutinho, Iago Aspas and Sturridge."
Monday's game will see Swans midfielder Jonjo Shelvey face his former team-mates for the first time since his £5million move from Anfield during the summer.
The former Charlton man has made a promising start to life in south Wales and Laudrup knows Monday's game will have an extra significance for his new signing.
He said: "He has had a very good impact and he has done well. From the first moment he has had a good attitude, but this is just the start, he is still young, he is a big talent and British.
"It's an important game for him, against his former club, and it will not be a game like all the rest for him, it will be a bit special.
"But once he is a few minutes in he will settle down and it will become like another game but Liverpool is a part of his life as well.
"I was surprised they were willing to sell him to us, but it is to our benefit."