Since joining forces at the start of the 2012 season, Bhupathi and Bopanna have played 14 tournaments together and won one - Dubai championships - in February.
They have good results to show as they have made five semifinals, including the three elite Master Series, but have been a flop at the big stage of Grand Slams.
Mukherjea argued that going by current form, Bhupathi and Bopanna don't hold out much promise.
"On present form, their chances are not that bright," Mukherjea told PTI after returning from Wimbledon.
"They did not do well at Wimbledon and also fared badly at the French Open. They will be up against players like Federer, Wawrinka, the Nadals and the Djokovics. So, going by the present form, the chances are not very good," he said.
In the last four tournaments, Bhupathi and Bopanna's best performance has been a quarter-final appearance at the Queen's Club event in London.
At Wimbledon, they were out in the second round and at Roland Garros they did not go beyond the first round.
However, it may be noted that Bhupathi and Bopanna had beaten the world number one pair of Max Mirnyi and Daniel Nestor at the Rome Masters, in May. Mukherjea said, much would depend on draw.
"Let's see, who they play in the first and second rounds. There is no surety on medal," Mukherjea said.
The former Davis Cupper also felt that Bhupathi and Bopanna would be under a lot of pressure to perform due to the selection controversy.
"They have a point to prove. Pressure will be on them to deliver after all the controversy," he said.
At the same time Mukherjea felt that controversy will not affect the players' performance.
"They are professionals. Once they are on court, they will forget all the differences," he said.
Indian tennis endured a huge furore after AITA initially chose Leander Paes and Mahesh Bhupathi for the men's doubles event. Both Bhupathi and Bopanna refused to partner Paes, insisting on being sent as a team to London.
A cornered AITA agreed to team up Bhupathi and Bopanna while Paes was given the young Vishnu Vardhan as partner. In compensation, Paes was assured that he will be teamed up with Sania Mirza for the mixed doubles.
Sania was keen to play with Bhupathi, with whom she won two Grand Slam titles, but agreed to play with Paes.