GB's 2008 men's 4x400m relay team moved up from fourth to third after Russia's Denis Alekseyev failed a drugs test when his sample was retested.
It had been suggested the medal ceremony could take place at the World Championships in London in August.
But next month's Anniversary Games also take place at London's Olympic Stadium.
A decision is yet to be made on when Rooney and team-mates Andrew Steele, Robert Tobin and Michael Bingham will receive their medals.
Rooney, 30, told BBC Radio 5 live: "I don't want to be distracted. I need to go to the World Championships and focus on that, so if we could get it done at the Diamond League, I'd love that.
"There's no way of getting back to Beijing and doing it that way, but if we can go to an Olympic stadium and be in front of a British crowd, that would be amazing.
"But whatever happens, whenever it happens, I just can't wait to get on that podium."
The International Olympic Committee has reallocated medals from Beijing after Alekseyev and compatriots Anastasiya Kapachinskaya and Inga Abitova tested positive for banned substance Turinabol.
Britain's women's 4x400m relay team have also moved into the bronze medal position.
Christine Ohuruogu, Kelly Sotherton, Marilyn Okoro and Nicola Sanders finished the race fifth but have moved up to third as a result of both third-placed Russia and fourth-placed Belarus being disqualified due to subsequent failed tests.
The men's Beijing medals are in the possession of the British Olympic Association and British Athletics but an announcement is still to be made on where they will be awarded.
They could be presented at next month's Diamond League Anniversary Games, or at the World Championships in London in August.
But, as the World Championships is an IAAF event, the IOC would have to give permission for any presentation to take place as Olympic medals fall under their jurisdiction.
British Athletics does not have possession of medals for the women's 4x400m team yet as legal proceedings are ongoing regarding athletes in their race.
Britons Dame Jessica Ennis-Hill, Jo Pavey, Sotherton and Goldie Sayers are among those waiting to receive Olympic and World Championship medals they were denied by drugs cheats.
Sayers has told the Guardian she would be "gutted" if she did not receive her medal at the World Championships this summer.
Britain's Martyn Rooney says he would rather receive his Beijing Olympic bronze medal at the Anniversary Games than at the World Championships.