Bopanna, who is making a comeback after recovering from injury, had to sit out the Davis Cup tie against New Zealand in Pune last month which India won 4-1.
However, the All India Tennis Association (AITA), which announced the preliminary squad of six players here on Monday, omitted Saketh Myneni and Sumit Nagal, both of whom are recovering from injuries.
The final squad of four players will be selected two weeks before the tie, which starts on April 7 in Bengaluru.
The AITA has also included two juniors in Dhruv Sunish and Nitin Kumar Sinha in the practice squad in order to groom them for the future.
This will be the first engagement for the Indians since former doubles star Mahesh Bhupathi took over as the non-playing captain.
"With the current roster of available players for the Davis Cup tie, I am confident this is the strongest squad for the tie," Bhupathi said.
"My decision on the final competing team for the weekend will be based on their performances over the next three weeks and their fitness levels during the week of the tie," he added.
"I look forward to a fruitful term as captain of the Davis Cup team, and count on strong support from the boys and the AITA."
With Indian players suffering from fitness problems during Davis Cup in the past -- especially in the singles matches -- Bhupathi has asserted that extensive fitness tests will be conducted before the final squad is selected.
"We have to make sure that the players who show up are going to be ready to play all three days if required, based on their fitness level and everything," India coach Zeeshan Ali said.
"Rohan had picked up an injury during the Chennai Open and carried it into the Australian Open. He had apparently recovered ahead of last month's Davis Cup tie against New Zealand.
"But three days after he joined the national squad, the injury played up again and he had to pull out.
"So we have decided to specially carry out mandatory fitness tests so that these issues can be detected beforehand.
"This will ensure that no player is carrying an injury when he comes into the squad. But if someone gets injured in the camp or during the match, it's a different matter," he added.
Paes and Bhupathi did not enjoy a cordial relationship during their playing days. Bopanna, who is closer to Bhupathi, also has had problems with Paes, most notably ahead of last year's Rio Olympics when he had initially refused to team up with the veteran doubles star.
Ali, however, was confident that the trio will put their differences aside and work in the interest of the national team.
"They have their issues. Everybody knows about that. But whenever in the past they have been called to play for the country, they have come forward.
"The fact of the matter is when it comes to the country there is no lack of commitment from either one of them," Ali said.
"Even in the Olympics, Rohan made his preferred choice of doubles partner known. But at no point did he say that if he is not going to get the player he wanted he was not going to play.
"So I think when it comes down to being professional tennis and the need to play with each other we have not seen any lack of commitment from either of them," he added.
"They have played some amazing matches for us in the past and I am hoping that they continue to do that."
AITA's selection committee chairman S.P. Misra admitted that Uzbekistan will be hard to beat, but was confident that the Indians will give a good account of themselves under Bhupathi's guidance.
"He has got vast experience of winning multiple Grand Slams. Hopefully, he will be able to guide the team very well. We have a lot of hope on him.
"Mahesh has recently stopped playing. A lot of the opponents our players will face are those who Mahesh has played in the past.
"That is a huge advantage which we will have in the form of the kind of advice which Mahesh will be able to give our players," Misra told IANS.
"Uzbekistan is a tough team. They have Denis Istomin who has been playing great tennis. He has beaten (Novak) Djokovic and is in great form.
"We have to give him credit for that. But then we are hoping that we can beat their number two singles player and then win the doubles," he added.
The former Indian team captain asserted that the singles players in the current squad have the ability to put up a good fight.
"We do have good singles in the squad at present. Ramkumar (Ramanathan) played very well during the tie against Spain and was excellent in the last tie against New Zealand," he said.
"In the match where it counted he won the last two sets 6-2, 6-0. Beating someone in a deciding tie in that squad is really tough.
"The boy is growing in confidence. We had kept him as a reserve for many years and he has come good now."
Misra also asserted that the AITA is grooming junior players in order to address India's traditional weakness in the singles ties.
"We are trying to groom some juniors. In the last Davis Cup tie in Pune, we asked two of the top juniors to play as practice partners.
"This time also we have taken the top two juniors as practice partners. So once these boys get to know what happens in a Davis Cup tie and what is required of them, they will get a lot of confidence that they can play with the seniors," he said.
"We have to see how and when a good crop of youngsters come up."
The squad: Leander Paes, Rohan Bopanna, Ramkumar Ramanathan, Yuki Bhambri, Prajnesh Gunneswaran, N. Sriram Balaji.