Retaining their crown is all but out of reach for Madrid, who have been linked with Athletic Bilbao goalkeeper Kepa Arrizabalaga, Chelsea duo Thibaut Courtois and Eden Hazard, Tottenham star Harry Kane and others.
Asked if Madrid need reinforcements, Los Blancos coach Zidane replied: "No, at the moment I do not want anyone.
"Until the 31st [of January] we will see, but not at the moment, why? Because I am happy with my squad."
Gareth Bale provided a timely reminder of what he is capable of after scoring twice in as many minutes to cancel out Daniel Wass' opener for Celta.
However, the hosts earned a share of the spoils at Balaidos thanks to Maxi Gomez's goal with eight minutes remaining after Keylor Navas saved Iago Aspas' penalty 10 minutes earlier.
The draw was Madrid's third consecutive LaLiga stalemate away from home – extending their winless run on the road to four matches.
"I have to detect the problem because I am responsible," said Zidane. "And I'll try and we will try.
"Lately we are not playing regularly. We do not play as we should. We have to have more confidence in our possibilities. Maybe we do not have enough confidence to play 90 minutes well."
The Frenchman added: "We're not going to talk about the league every weekend, if we lose points we cannot be successful. You have to go match by match and win them."
Madrid president Florentino Perez made his way down to the dressing room post-match, but Zinedine said: "He has gone to the dressing room to cheer on the team, nothing more."