Russia are banned from competing in the team event due to their nation's invasion and the ongoing war against Ukraine, but meaning Medvedev is starting his campaign in Australia in the ATP 250 event in Adelaide.
Medvedev and his compatriots were also banned from competing at last summer's Wimbledon championships after a decision was taken to exclude Russian and Belarusian players following the Ukraine invasion.
Now Medvedev has conceded he would rather be playing in the United Cup as he prepares for the first Grand Slam event of 2023 at the Australian Open.
"I would definitely prefer to play the United Cup," he said.
"We would definitely be good favourites. But it is what it is, and I'm happy to be here in Adelaide playing in this tournament.
"I completely understand why we are not playing Davis Cup or United Cup and team competitions where we would represent our country. Hopefully, I can play the individual events. I play what I can play, so here I can play Adelaide, and I'm really happy about it. I want to show my best tennis."
Medvedev could be on course to meet Novak Djokovic in Adelaide, after the duo were placed in the same half of the draw to throw up the prospect of rematch of the 2021 US Open final.
"I'm motivated to be in the (Adelaide) semis - and if it's Novak there, it's great," added Medvedev added.
"If it's somebody else who beats him, I don't care much. I just want to be in the semi-finals to start, and I don't care who I play.
"I feel like everybody is a little bit nervous, and that's normal. This feeling of the first tournament of the year is really special. I like playing in Australia, so really looking forward to it."
Meanwhile, Belarus' world No 5 Aryna Sabalenka has admitted she missed Wimbledon last year and suggested the ban on players from her nation did not help the political crisis in Ukraine.
"We're just athletes playing their sport. That's it. We're not about politics. If all of us could do something [about the war], we would do it, but we have zero control," she told the Australian newspaper The Age.
"They banned us from Wimbledon, and what did it change? Nothing - they are (Russian government) are still doing this, and this is the sad [part] of this situation."
When asked about her absence from Wimbledon last summer, Sabalenka offered up this emotional response.
"It was a tough time. I was super disappointed with their decision," she said.
"I really missed the people because the atmosphere at Wimbledon is super amazing. You can feel these people really love tennis there, and I really miss them.
"I really hope that I'll play there [in 2023], just because of the people, to feel this atmosphere. But if they're going to ban us again… I don't care about Wimbledon's decision. The only thing I'll miss is the people."