Real Madrid remain cautious over the possible signing of Kylian Mbappé, sources have told ESPN, but the club are also hopeful that a deal could finally be done to land the Paris Saint-Germain forward this summer.

There is a reluctance to talk openly about the arrival of Mbappé at the Bernabeu after last summer's abrupt U-turn that saw the France international agree a new contract with PSG when he had been on the verge of a move to Madrid.

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The club's public position is that their transfer market activity has been completed after the signings of Jude Bellingham, Joselu, Fran García and Brahim Díaz. However, the reality is that the club has left vacant the No. 9 shirt that belonged to Karim Benzema before his departure for Al Ittihad because there is also hope that Mbappé could become available.

Sources have told ESPN there has been no notable progress since Mbappé announced on June 12 that he had informed PSG that he would not be exercising an option to extend his contract beyond 2024.

In public, Mbappé continues to insist that he wants to continue at PSG for one more season, but multiple sources have told ESPN that the player wants to sign for Madrid this summer, that PSG would like to avoid losing him on a free transfer next year, and that Madrid are willing to make a significant effort to see Mbappé lead their attack alongside Vinícius Júnior and Rodrygo.

Madrid are on alert and hopeful that their long-term pursuit could bear fruit this summer, in the knowledge that PSG would like to ease their spending in line with financial fair play restrictions.

A source told ESPN that a drawn-out summerlong transfer saga is not expected this time.

Madrid coach Carlo Ancelotti wanted to see his forward line strengthened last summer with a back-up to Benzema, and that need is even greater now that the Ballon d'Or winner has left for Saudi Arabia.

The Italian coach views Spain international Joselu -- signed on loan from Espanyol -- as an alternative rather than a starter, and the fact that he was assigned the No. 14, rather than Benzema's No. 9, suggests that the club have not closed the door on another arrival.

Madrid failed to defend their LaLiga and Champions League titles last season -- winning the Copa del Rey, the UEFA Super Cup and the Club World Cup -- and there is pressure to improve next campaign.

That pressure is increased given that the club plan to unveil their newly rebuilt Bernabeu stadium in December, the completion of a crucial project for president Florentino Pérez.