Former France youth international captain Darnel Situ has completed his move to Swansea City.
The 19-year-old defender joined Swansea from French club Lens on a two-year deal in August for a fee of £250,000.
But as the deal was not completed inside the summer transfer window.
Swansea therefore had to wait until the opening of the January transfer window to finalise the move, but Situ is now eligible to face Arsenal on Sunday.
Situ, who was a target for Manchester United, Chelsea and Liverpool as a youngster, has trained with the Welsh club since arriving in August.
Rodgers has also been linked with a loan move for Chelsea's England Under-21 midfielder Josh McEachran and is expected to complete his capture within the next 48 hours.
But he insists "there won't be many more" as the Swans boss strengthens his squad for their Premier League survival bid.
"Any of our business we'll do early on," said Rodgers.
"And it shouldn't go on more than that. There won't be much more."
Rodgers has also warned Swansea's top-flight rivals he has no intention of letting any of his top players leave the Liberty Stadium this month.
Wales international defenders Ashley Williams and Neil Taylor have been the latest Swansea players linked with moves away from south Wales, to Newcastle and Arsenal respectively
But Rodgers said: "I'm sure there will be a raft of players linked to clubs in the coming weeks but we want to keep our best players.
"The spirit is unique at this football club and the players can see the progress they are making here as individuals.
"There is a lot of speculation and in a way it's great because it shows the players are doing well.
"But they also understand that it comes on the back of performing well.
"It's nice for them to be recognised but they know they are at a great club that is moving forward and they understand that speculation is part of this business. We don't take too much notice of it."