The finance ministers of the US, Canada, the UK, Japan, Germany, France and Italy will meet in Dresden on Thursday and Friday for talks.
While the Greek situation isn't formally on the agenda, it's thought that the country's debt problems are likely to be discussed on the sidelines by G7 ministers.
"I would expect the Americans to put pressure on the Europeans in Dresden about Greece," the official was quoted as saying by Reuters.
"The Americans are stressing the geopolitical risks and telling us we have to find a solution, that we cannot really put the euro area and Europe at risk because of Greece."
There were also concerns among G7 nations about the impacts of Greece potentially asking Russia for some form of financial aid if the stalemate between Athens and its creditors continues.
"If Greece for some reason were to turn to Russia and Moscow would get involved more, they could get too much influence inside NATO and inside the EU when it comes to policies towards Russia," the official said.
With Greece struggling to make public salary and pensions payments, there are growing concerns that unless a deal can be struck between Alexis Tsipras' government and creditors, Greece may not be able to pay a $328 million (€300 million) installment to the IMF, due on June 5.
Despite the concerns over Greece's approach to negotiating new reforms that would unlock more financial aid from Eurozone partners and the IMF, there has also been criticism of the actions of the creditors, who have been accused of making a deal impossible, due to their conflicting demands and motives.
While understanding the American concerns over a potential Greek collapse, the official said that bowing to Greek demands without securing reforms properly would set a dangerous precedent.
"If Greece is bailed out without any conditions, after everything they have done, after having broken all possible commitments and not respecting any obligations, that would also have a very fundamental impact on the future and functioning of the Eurozone," the official said.
"If that becomes accepted, I don't know what follows."