French President Emmanuel Macron made similar appeals to Trump during his three-day state visit this week.
He has criticised Merkel for opening German borders since 2015 to a mass influx of mostly Muslim refugees, while she has watched with dismay Trump's decision to withdraw from the Paris climate accord.
Grenell, who has been strongly critical of the nuclear agreement, is a Republican foreign policy writer and commentator who was an aide to Trump's new national security adviser, John Bolton, when Bolton was former Republican President George W. Bush's ambassador to the United Nations.
The Iran deal, looming United States tariffs on European steel and aluminium products, a planned Russian gas pipeline running under the Baltic Sea to Germany, and Berlin's military spending are issues that divide Merkel and Trump and likely to come up at their working lunch.
"From today s perspective, we must assume that the tariffs will come on May 1", said a German government source. "It is important to cultivate this relationship".
The stylistic differences between the Macron and Merkel visits are "very telling" according to Mona Krewel of Cornell University.
Germany expects that tariffs on steel and aluminum imported from the European Union to the USA will begin on May 1, according to reports Thursday. But they said Germany would try to negotiate a broad package including other industries.
"There is a special responsibility that all United States officials have to reject partisan politics when they take government service jobs", he said.
"I don't think we should raise the bar of expectations too high", said Peter Beyer, coordinator of trans-Atlantic relations for Merkel's conservative Christian Democratic Union.
This will be Merkel's second trip to Washington, D.C., since Trump became president and her first since being re-elected last month as chancellor.
Cautious Merkel has failed to establish as strong a rapport with Trump as she did with Barack Obama and the mood music of her visit is likely to contrast sharply with that of Macron's "bromance" with the USA president.
Earlier this month, she acknowledged that the Nord Stream 2 pipeline, which would bring gas from Russian Federation directly to Germany, "is not just a business project".
Trump could seize on this, as well as Germany's slow progress in moving closer to the North Atlantic Treaty Organisation defence spending target.
The Berliner Zeitung daily looked ahead to Merkel's tough diplomatic mission just after Macron's charm offensive, saying that "she can hardly follow Macron's best-buddy act, but she does need a strategy".
Her relationship with Barack Obama was particularly close, officials from that administration have said, so much so that he was a powerful voice encouraging her to run for a fourth term.