Real Madrid are in talks with Paris Saint-Germain forward Kylian Mbappé over signing on a free transfer this summer and are optimistic about concluding a deal soon, sources told ESPN.

ESPN reported Thursday that Mbappé has informed PSG that he would be leaving as a free agent when his contract expires at the end of this season, after deciding that his future lies in Madrid.

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Madrid submitted a formal contract offer to the France international last month, while PSG were still hopeful of convincing their star player to stay.

Sources told ESPN that Madrid were now hopeful of finalising an agreement in the near future, but a contract is yet to be signed, with some details still needing to be ironed out.

Mbappé started PSG's 2-0 win at Nantes in Ligue 1 on Saturday on the bench, before coming on to score a 78th-minute penalty. He also scored in the French club's 2-0 victory over Real Sociedad in last week's Champions League round-of-16 first leg.

The forward has scored a total of 32 goals in all competitions this season, despite the constant speculation about his future.

Mbappé has long been Madrid's top transfer target, and after being on the brink of signing him in 2022 -- before a change of heart saw Mbappé sign a contract extension at PSG -- the LaLiga giants are now closer than ever to landing the World Cup winner.

Madrid are top of LaLiga on 62 points, six ahead of nearest rivals Girona, who play on Monday, and beat RB Leipzig 1-0 away in their Champions League round-of-16 first leg last week.

Their top scorer in the league this season has been midfielder Jude Bellingham, with 16 goals, followed by Joselu and Rodrygo with eight, and Vinicius with seven.

Information from ESPN's Alex Kirkland contributed to this report.