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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Mr Hofer, 45, won last month's first round but failed to avoid the run-off.
If he wins on Sunday, Mr Hofer could become the EU's first far-right head of state, although Austria's president plays a largely ceremonial role.
On Thursday, the two rivals traded accusations during a TV debate.
Mr Van der Bellen, 72, accused Mr Hofer of wanting to dismiss any government that did not suit him.
He was referring to the fact that, despite limited powers, the president can sack governments and also swears in chancellors.
Mr Hofer countered that Mr Van der Bellen was the one who had refused to swear in a Freedom Party chancellor if the party won at the next general election in 2018.
However, the debate was said to be less feisty than last Sunday's TV encounter, described by some commentators as a slugfest.
In the first round of voting, Mr Hofer secured 35% of the votes, while Mr Van der Bellen, polled 21%.
For the first time since World War Two, the candidates from Austria's two main parties - the Social Democrats and the People's Party - did not make it to the run-off.
Both parties have governed Austria for decades - either alone or in coalition.
This is a big shake-up in Austrian politics, as the country has had a president from the centre-left or centre-right since 1945.
The victory in the first round of the far-right candidate reflects widespread discontent with the status quo, as well as concerns about immigration and the economy, correspondents say.
Support for the Social Democrats and the People's Party has been falling in recent years.
In the last general election in 2013, the two parties won just enough votes to govern in a "grand coalition".
Incumbent President Heinz Fischer, 77, cannot run again after two terms in office.
Mercedes say they are "optimistic" Nico Rosberg will avoid a grid penalty after the gearbox problem that afflicted him at the British Grand Prix.
[NEXT_CONCEPT]
Austria's far-right Freedom Party presidential candidate Norbert Hofer and his rival, Green-backed Alexander Van der Bellen, are holding final rallies ahead of a run-off vote.