As we head towards the end of the summer transfer window, further drama involving Liverpool and PSG could await us. New reports from Mundo Deportivo have surfaced with only a few days left in August. These reports claim that Liverpool have joined the race to sign PSG forward Kylian Mbappe and are ready to rival Real Madrid in this race to secure Mbappe’s signature.It seems the Premier League team have already made contact with Paris Saint Germain and are seeking the possibility of a late swoop. Kylian Mbappe is believed to be a big admirer of Liverpool and as Liverpool have barely made any transfers this summer window, it puts them in a better position to sign the French international than any other English club at the moment..@DuncanCastles: "Liverpool has a special interest to Kylian Mbappe. He supported Liverpool when he was younger - he likes the way they play football." #awlive [transfer window podcast] pic.twitter.com/cG9gL8Xojy— Anfield Watch (@AnfieldWatch) August 24, 2021Liverpool’s arch-rivals Manchester United, on the other hand, have recently completed the sensational signing of Cristiano Ronaldo. Manchester United's local rivals, Manchester City, it seems, are now holding out for next summer to target Erling Haaland. They broke the Premier League transfer record earlier this summer by bringing in Jack Grealish from Aston Villa.Liverpool plan on strengthening their squad by signing PSG attacker Kylian MbappeKylian Mbappe in action for PSGChelsea have brought in Romelu Lukaku this season while Tottenham have convinced Harry Kane to stay at the club which leaves Liverpool as the only English club yet to make a marquee signing this season. This has caused quite an uproar from Liverpool fans as many seem to think that the Reds do not have enough quality to challenge for the Premier League.The addition of Kylian Mbappe to Liverpool’s squad will help them strengthen their team and would go a long way in silencing the critics. The Frenchman would be an upgrade on Liverpool’s current striker, Roberto Firmino. This could form a very deadly offensive combination for Liverpool with a front three of Kylian Mbappe, Mohamed Salah and Sadio Mane.Real Madrid are confident of luring Kylian Mbappe away from PSG, but they are wary of possible competition from Liverpool 🔊👇pic.twitter.com/tQhJovjGrS— Sky Sports Premier League (@SkySportsPL) August 25, 2021The Reds, however, are racing against time as Real Madrid are on the cusp of signing Kylian Mbappe. A recent report suggests that Los Blancos have almost reached an agreement with PSG to sign the player, having made an astounding €180 million offer for the PSG forward. The Ligue 1 giants are most likely to accept this deal as they do not want to risk losing the striker for free next season.