Real Madrid made a bid for Kylian Mbappe, Paris Saint-Germain's, at 137m (160m).
La Liga made an offer Sunday, and Paris Saint-Germain have yet to reply.
Mbappe will be out of contract at Parc des Princes next season and has refused to sign a new contract despite PSG's efforts to get France international to commit his future to this club.
PSG has heard from the 22-year old that he dreams of playing for Real Madrid. Real Madrid have been linked to a move for the World Cup winner during the summer transfer window.
Use Chrome browser to access a better video player. Kaveh Solhekol, a major agent in football, tells The Transfer Show that he is trying to arrange a deal that would see Kylian move to Real Madrid and Cristiano Ronaldo go to Paris Saint-Germain.
Mbappe scored 133 goals and provided 63 assists in 174 matches for PSG in all competitions. This has led them to 11 major domestic honours including three Ligue 1 titles.
He was originally loaned from Monaco for a season in 2017, and was then signed permanently for 165.7 million a year later.
Mbappe started all three Ligue 1 games for PSG this season and has made two assists. On Friday, he scored his first goal of the campaign, scoring in a 4-2 win against Brest.
Sky Sports News was informed by one of the most powerful agents in the game that he is trying to broker a deal that would see Mbappe join PSG and Cristiano Ronaldo move to Real Madrid.
Ronaldo will also be out of contract in the summer. He has not yet told Juventus he is leaving, but the Serie A club won't stop him if another club offers him a place.
Image: Kylian Mbappe and Angel Di Maria scored once each in PSG’s 4-2 victory over Brest
Real Madrid boss Carlo Ancelotti said last week that Mbappe's club was interested in him as he heads into the final stages of the transfer window.
"I don’t care about what will happen. My team is very strong and I am very grateful for them. They bring me joy. That is what I am focused on.
"Let's just wait for these 10 days, and then I will be focusing on the team I have."
Mauricio Pochettino, the head coach of PSG, said about Mbappe prior to their match with Brest: "Kylian. I see him being very healthy. He is working hard to be ready for this season. He'll be with us all season.
"We also know that during these times, many things are said. Some things are possible, while others are not. He's focused and working well. He's focused."
Leonardo, the sporting director at PSG has denied any claims that Mbappe could be leaving. However, former Real Madrid manager Zinedine Zidane as well as Luka Modric, have suggested that he might one day play for them.
Use Chrome browser to access a better video player Spanish journalist Alvaro Montero claims Real Madrid are closer than ever to signing Paris Saint-Germain forward Kylian Moappe
Real Madrid lost an estimated 257m (300m), in the coronavirus pandemic. They signed David Alaba, who was the only new player to join their team during the current transfer window.
PSG signed Lionel Messi in August. Achraf Hakimi and Sergio Ramos also joined the side of Pochettino. Georginio Woijnaldum was also involved.
Sky Sports has the summer transfer window.
Follow all the latest news and rumours about transfer in our Transfer Centre blog on Sky Sports' digital platforms. You can also keep track of all developments on Sky Sports News.
