Mbappe wore a white baseball cap and white T-shirt, and whether by accident or design that only fuelled anticipation of a blockbuster move to Los Blancos.
According to reports in Spain, Madrid has offered €170 million ($275.6 million) plus €10 million ($16.2 million) in add-ons for the France striker.
Mbappe was pictured by El Chiringuito TV arriving at the PSG premises ahead of a scheduled training session.
He was reported to have arrived shortly after 9:30am local time, with PSG due to step up preparation for its Ligue 1 clash with Reims on Monday (AEST) evening.
Mbappe, 22, has entered the final year of his PSG contract and there has been no indication of a desire on his part to extend his stay. He would be able to leave on a free transfer at the end of the current season, were he not to agree new terms.
The 2018 FIFA World Cup winner joined from Monaco in 2017 and has scored 133 goals in 174 games for the Paris side, at a rate of one goal every 102.46 minutes.
He has scored six hat-tricks for PSG and would join up with France team-mate Karim Benzema in Madrid's attack should the move to Spain go through.
PSG sporting director Leonardo was also pictured making his way into the training facility.
Earlier this week, Leonardo expressed dissatisfaction as the saga unfolded, with PSG having heavily invested during the close season to assemble a formidable squad.
It has brought in Lionel Messi from Barcelona in a staggering move, as well as acquiring the likes of Sergio Ramos, Gianluigi Donnarumma, Georginio Wijnaldum and Achraf Hakimi.
Messi could make his debut against Reims, but that factor was being overshadowed by the prospect of PSG possibly losing Mbappe, a player it hoped to build the team around for years to come.
Leonardo said on Thursday (AEST): "We cannot be happy with this situation, because we did something this summer, we have created a dream, we will not let anyone destroy it or position themselves above the club.
"Kylian is at the centre of the project but not above it. We created a positive atmosphere, a desire, an emotion. That was our plan."
Among players from Europe's top five leagues, only Messi and Bayern Munich's Robert Lewandowski have had more goal involvements – scoring and assisting – than Mbappe since the PSG frontman made his debut for the Parisians in September 2017.
Messi has had 236 involvements, Lewandowski 213 and Mbappe 191, with Cristiano Ronaldo (172) ranking fourth on the list.