Leeds United have brought in 11 signings this summer.
Cameron Borthwick-Jackson joined on loan from Manchester United this week in what was Leeds' 11th transfer so far this summer.
The Yorkshire Evening Post reported on Thursday that Christiansen was still in the market for a striker, claiming that the Whites were looking at Hamburg's Pierre-Michel Lasogga.
However, when asked by LUTV whether he was happy with his squad or if there would be further arrivals, the 44-year-old said: "I am happy."
He went on to add that he was "very satisfied" with the signings that he has made.
It was previously suggested by The YEP that United - who have signed Matthew Pennington on loan - would get an additional centre-back in, but Liam Cooper's contract extension this week might suggest that Christiansen views him as a viable option.
Borthwick-Jackson can also operate in central defence, while former Under-23s centre-back Conor Shaugnessy has looked good since stepping up into the senior side.
Leeds, who have scored seven goals in their first two matches, host Preston North End at a sold-out Elland Road on Saturday as Christiansen's side look to extend the feel-good feeling.