Djokovic, who was playing in his first tournament of the season following the controversy that surrounded his Covid-19 vaccination status at the Australian Open last month, has held the No 1 ranking since February 2020.
The Serbian had to better Medvedev’s result at the Mexican Open in Acapulco this week but with the Russian already through to the last eight, he is guaranteed to lose the number one spot.
Medvedev, the US Open champion, will become the 27th male player to reach the top spot after Djokovic was beaten in a shock 6-4 7-6 defeat to world No 123 Vesely.
The 26-year-old Medvedev also becomes the first world number outside of the big four of Djokovic, Rafael Nadal, Roger Federer and Andy Murray since Andy Roddick in 2004. His position will be confirmed when the rankings are updated on Monday.
Djokovic, who has held the position at the top of the men’s rankings for a record 361 total weeks, said before the tournament in Dubai that he would congratulate Medvedev if the Russian replaced him as number one this week.
“It’s in his hands. He deserves to be No 1,” Djokovic said before his season debut. “Eventually it’s going to happen. If it happens this week, I’ll be the first one to congratulate him.”
The Serbian remains unvaccinated for Covid-19, which could limit his tournament appearances on the ATP Tour this season with many events only allowing vaccinated players to compete.
The Dubai Duty Free Championships, where Djokovic is a five-time champion, did not have a mandate on Covid vaccinations but upcoming tournaments such as ATP Masters events in Indian Wells and the Miami Open next month will require players to show proof that they have received the jab.