Trump's commitment to the military alliance has been less than convincing, calling it both "very important" to him and "obsolete because it isn't taking care of terror" in a recent interview with the New Yorker.
Public support for joining Nato in non-aligned Sweden has moved back and forth in recent years, with opinion regularly shifting on the matter in 2016, but the country does have a close relationship with the alliance, including being part of a Host Nation Support Agreement, which allows Nato to transport helicopters, aircraft and ships across Swedish territory upon Sweden's invitation.
But Trump's unorthodox position for a US President on Nato could change things, according to Mike Winnerstig, security policy expert at the Swedish Defence Research Agency (Totalförsvarets forskningsinstitut).
"It depends on what Sweden wants. The current government has built up a strong relationship with Nato without planning for membership, and at the same time built up a bilateral relationship with the USA which is not based on defence guarantees, but which it is in any case hoped would include some kind of American protection of Sweden if we got involved in armed conflict," he told The Local.
"That was largely built through the Obama administration's very positive attitude to Sweden. There is nothing to suggest that the Trump administration is going to have an equally positive view of Sweden – in part because we spend very little on defence and in part because we spend our money on things Trump has tended not to appreciate, like a strong welfare state and high immigration."
Trump has criticized Nato members for not paying “what they're supposed to” for US protection through the alliance, and according to Winnerstig, that casts even greater doubt over whether his administration would aid a non-member like Sweden, which spends relatively little on defence.
"If Trump implies that Nato countries which don't spend two percent of their GDP on defence will not be able to automatically count on American help despite the Nato guarantee, then the risk is much greater that the USA will not come to the aid of countries which aren't even in Nato and pay even less."
A Swedish government report last year concluded that Sweden would likely be accepted as a Nato member if it applied, and that the process would take around 12-15 months.
But could Trump's favourable view of Vladimir Putin change that dynamic?
"If Sweden wants to become a NATO member in the future, Trump's until now positive view on Russia under Putin could be a problem. It isn't certain that he would want to see Nato grow in general, especially on account of Russia," Winnerstig observed.
The defence expert emphasized however that while Trump will evidently be an important player in the alliance, he is not the only influence.
"The American president is always an important player within Nato. However, he is not an absolute master, but in principle one of 28 heads of government who all have the equivalent of a veto when it comes to the issues it takes a position on. It would be difficult for him to impact our current level of cooperation with Nato, which of course doesn't include defence planning or defence guarantees."
Swedish Foreign Minister Margot Wallström recently poured cold water on the idea of applying for Nato membership, saying that more political dialogue, increased defence capabilities and broad bilateral partnerships are the country's answer to rising tensions in the region.
The centre-right opposition Moderates are in favour of joining however.