Los Blancos are four points ahead of rivals Barcelona ahead of the final two rounds of the competition and can claim the title with victory at home against Villarreal on Thursday.
If not, Zinedine Zidane's side will have another chance in their final fixture away to Leganes on Sunday, with just two points needed overall.
Fans usually flock to the famous fountain in the centre of the Spanish capital when Real Madrid win a major trophy and wait for the players and coaches to arrive in celebrations which last long into the night.
But in the current situation caused by the coronavirus pandemic, Madrid have discouraged their supporters from gathering in large numbers.
"We are all aware of the difficult situation that we are experiencing and the efforts being made across society to counter the impact of the Covid-19 pandemic," Madrid said in a statement on their website on Tuesday.
"Football is also playing its part in this and, with everyone's help, we managed to resume the competition in extremely complex circumstances.
"With just two matchdays of the LaLiga season to be played, both our team and F.C. Barcelona have a chance of being crowned champions.
In the event that Real Madrid are crowned champions, our players will not visit the usual points of celebration, in particular, the Plaza de Cibeles and we therefore also ask our club members and supporters that, in the event that we secure the title, they do not gather in these places.
"In this regard, all of us must make a contribution, as has been the case to date, and show the utmost responsibility to avoid the risk of contagion."
The club went on to thank their fans for the support, but added that it is impossible to celebrate all together in the current situation.
"All of the effort and work put in by our players, coaching staff and the club towards this possible title success has always been done with a view to sharing the triumph with our fans, but we are aware that the current situation obliges us to maximise the necessary precautionary measures," the club said.
"Real Madrid feels the duty to issue this important call in a show of utmost responsibility and with the firm belief that any possible triumph involving our team must not give rise to a massive backward step in the battle we are all waging against this pandemic."