The two leaders will meet at the PM's offices in Rosenbad, central Stockholm around lunchtime, and after a week in which the new US President signed off on a number of controversial executive orders, the talks are timely.
Merkel spoke with Trump over the phone last Saturday on issues like relations with Russia, the situation in the Middle East and NATO, while she also reminded the American of his human rights responsibilities according to the Geneva Refugee Convention.
Since then, the German Chancellor has stepped up her public criticism of the travel ban Trump placed on visitors to the US from seven predominantly Muslim countries, saying the fight against terrorism "in no way justifies general suspicion against people of a specific faith, in this case people of the Muslim faith or people of a certain background".
"This approach in my view contradicts the basic tenets of international aid to refugees and international cooperation," she added.
Löfven has yet to comment on Trump's move by contrast, though his colleague, Swedish Foreign Minister Margot Wallström, has called it "regrettable". The Swedish PM will no doubt be pressed on the issue when he and Merkel hold a joint media conference following their meeting.
Sweden and Germany already have good relations at present, but cooperation between the two will be even more important going forward with the UK set to leave the EU. When Brexit finally occurs, Sweden will lose one of its closest allies in Europe, so strengthening other alliances and building new ones is particularly important for the Nordic nation.
"We are still facing many major challenges in Europe, and it is important for Sweden to be able to cooperate with Germany for more jobs and higher growth, for security, and to ensure that the EU is better able to deal with the refugee situation," Löfven said in a statement ahead of the meeting.
Löfven and Merkel will soon meet again on February 3rd at an informal meeting of EU heads of state or government in Valletta, Malta, where refugee policy and the future of the EU without the UK is on the agenda. Tuesday's meeting in Stockholm will therefore give the two leaders a chance to discuss those issues before tackling them collectively with other EU leaders later in the week.