The Russian tennis star reached the top of the rankings for the first time earlier this year but has suffered this summer after being banned from taking part in Wimbledon due to his country's invasion of Ukraine.
Medvedev is currently in action at the Los Cabos Open in Mexico and confessed that Rafael Nadal is likely to usurp him in the rankings by the end of 2022.
He told the ATP website: "Number one? Obviously I will try to do what I can but it also depends on others, I am aware that to defend the title I would have to win all the remaining tournaments and therefore I believe that at the end of the year Rafael Nadal will be the number one in the world."
Medvedev won his first major title at the US Open last year and is targeting more success during the North American hard-court season.
He said: "In the meantime, I will try to keep it for a long time, in North America I have always done well and I want to continue like this."
Medvedev explained that he will simply try and win matches so he can remain at the top of the rankings.
He said: "It's always different, but it is certainly important for me now to win games.
"Each opponent can be very difficult, so I can say that the more matches you win and the more confidence you can gain, you start to feel your game better and this is what I will try to do in the Los Cabos tournament."