Rome, May 16 : Carlos Alcaraz's early exit from the Italian Open with loss against Fabian Marozsan has repercussions beyond the Rome ATP Masters 1000 event and it also could have a big effect on the battle for No. 1 in the ATP Rankings.  The Spaniard will return to World No. 1 next Monday, but instead of departing the Foro Italico with a sizable advantage, Alcaraz may be left with only a narrow lead if Novak Djokovic and Daniil Medvedev push on to have deep runs in the Italian capital. If Djokovic and Medvedev both lose in the fourth round on Tuesday, Alcaraz will lead Djokovic by 950 points and Medvedev by 1,395 points. But both stars can claim plenty of points on the Italian clay. Djokovic, a six-time Rome champion, can reach 6,775 points by the end of the tournament, which would bring him within 40 of Alcaraz's 6,815. Since both men lost in the quarter-finals at Roland Garros last year and will therefore drop the same number of points (360), that would set up an epic World No. 1 battle in Paris. But do not count out Medvedev, either. The former World No. 1 has admitted to feeling more comfortable than ever in recent weeks on clay. The 27-year-old would reach 6,330 points with a title in Rome, putting him 485 points behind Alcaraz. Medvedev reached the fourth round at Roland Garros last year, so he will drop 180 points, which would bring him within 305 points of the Spaniard in the ATP Live Rankings when play begins in Paris. With the North American summer hard-court season still to come, Medvedev would be in a good position to make a charge for No. 1 in the weeks and months ahead. If Djokovic reaches the Rome final, Medvedev cannot pass him for World No. 2 next Monday. If the Serbian does not, the World No. 3 will have an opportunity to ascend one spot. At the same time, a maiden ATP Masters 1000 title for Casper Ruud could propel the Norwegian to World No. 3 depending on Medvedev's results. Nothing that happens the rest of the Italian Open can stop Alcaraz from returning to World No. 1. But Djokovic and Medvedev can make the coming weeks even more interesting in that battle with a deep run in Rome. It is also worth keeping an eye on the ATP Live Race To Turin, which serves as a barometre for the year-end No. 1 battle. Alcaraz is first with 3,455 points, but Medvedev (3,390 points) can take his spot with a win over Alexander Zverev or J.J. Wolf on Tuesday evening. Djokovic (2,655 points) would need to win the title to pass Alcaraz's point total. /IANS