Rafa Nadal, beaten in the quarter-finals, has dropped to 10th, his lowest position for 10 years.
Djokovic might have to do a lot of scurrying for the ball against Wawrinka, which can cause him trouble.
Williams wins her 20th Grand Slam as she beats 13th-seed Safarova 6-3, 6-7, 6-2 for her 3rd French Open title.
Serena Williams wins her third French Open title after 6-3 6-7 6-2 win over Lucie Safarova in final.
Djokovic already owns eight major titles, but none from Roland Garros, where he lost the 2012 and 2014 finals to Rafael Nadal.
Wawrinka overcame strong resistance from Tsonga to win 6-3 6-7 7-6 6-4 and reach the final.
Ailing Serena wins 10 straight games to beat Timea 4-6, 6-3, 6-0 and set up a French Open final against Safarova.
Nadal came into the French Open ranked 7th and without a European claycourt title for the first time in 10 years.
The twice Roland Garros champion set up a meeting with Swiss 23rd seed Timea Bacsinszky or Belgian Alison van Uytvanck.
Ivanovic reached her first Grand Slam semi-final in seven years when she beat Ukraine’s Elina Svitolina 6-3, 6-2.
Czech Republic’s Lucie Safarova knocks Maria Sharapova out of the French Open to enter her first quarter-final.
Women’s doubles pair Sania Mirza and Martina Hingis enter quarter-finals of the French Open.
Nishikori will play Frenchman Jo-Wilfried Tsonga after the 14th seed beat Czech fourth seed Tomas Berdych in four sets.
Ana Ivanovic will play Elina Svitolina in the last-eight at Roland Garros.
Eighth seeded Indo-Swiss pair went down fighting to Slovenian Srebotnik and Romanian Tecau 7-6, 3-6, 6-10 on Saturday.