If the team had to change the gearbox as a result of damage from Silverstone, Rosberg would be hit with a five-place grid penalty in Hungary this weekend.
Mercedes said Rosberg would run the gearbox in practice on Friday at the Hungaroring "to make sure it is OK".
A spokesman added: "We are optimistic that it will be."
Rosberg was demoted from second to third place at Silverstone after Mercedes were found to have broken rules restricting radio information given by teams to drivers as they tried to help him fix the problem.
The German heads into the weekend with a one-point championship lead over team-mate Lewis Hamilton.
Mercedes have not won the Hungarian Grand Prix since the start of their domination of F1 following the introduction of turbo hybrid engines in 2014.
Hamilton holds the record, jointly with Michael Schumacher, for most wins at the Hungaroring, with four victories.
Rosberg has never finished higher than fourth at the track.
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Mercedes say they are "optimistic" Nico Rosberg will avoid a grid penalty after the gearbox problem that afflicted him at the British Grand Prix.