Trump has espoused "an unusually Russia-friendly foreign policy, to the extent that his domestic opponents have labelled him as President Vladimir Putin's favoured candidate," BMI said in a new report.
In July, Donald Trump began questioning the US' commitment to Nato, an alliance hailed by its supporters as having maintained peace since World War 2.
He has since called it "obsolete". Add that to his lavish praise of Russian president Vladimir Putin and you've got a recipe for a new era in US-Russian relations should he claim the White House in November.
Hillary Clinton, on the other hand, "would be likely to harden US policy towards Russia with a view to containing its influence", BMI said.
For some background: In the aftermath of WW2 and the start of the Cold War, the US embarked on a policy of containment - literally trying to geographically contain the spread of communism. Since the Soviet Union disintegrated, the West has sought to entice former satellite states into Nato and the EU.
With Putin's rise Russia has been far more aggressive in resisting these moves, typified in the annexation of the Crimea and unrest in the Ukraine. There's also the small matter that Putin and Russia are friendly to President Bashar al-Assad, which the West thinks needs to be out of the picture for a resolution in Syria.
This means that the next US President inherits a fairly bitter relationship, according to BMI.
It thinks Clinton is more than President Barack Obama internationalist in her hopes to promote American values and this would lead to a deterioration of relations - with Clinton not easing sanctions, for example - as Russia takes a wary view of her presidency.
But, BMI states, Trump offers the prospect of rapprochement, having questioned commitment to Baltic states in the face of perceived Russian aggression.
This would mean Russia could see opportunities to take back former states - such as Belarus, Ukraine and Moldova - into its sphere of influence.
Or as the analysts put it: "This would pave the way for a reduction in the military build-up in Eastern Europe since 2014, and new treaties to protect these new geopolitical realities. In return, Russia could increasingly align with the US as a counterweight to China and co-operate more closely against Islamic State.
However, as we discussed previously, there are multiple obstacles to establishing a de facto buffer zone between Russia and the West in Eastern Europe. Firstly, the US and EU would be extremely reluctant to formally concede a Russian sphere of influence over Eastern European countries, even if their prospects of NATO and EU membership are very poor.
Secondly, the complexities of formalising these putative arrangements mean that they would take years to agree upon.
Thirdly, sudden political changes in Eastern Europe, such as a popular uprising in Belarus or conflict in Moldova, could negate moves towards these new arrangements.
But BMI does concede that it may not all end up cheery, given Trump's commitment to the US military and how he could get beaten down in the US congress.
"There is also a danger than Russia could misinterpret carefree comments by Trump on geopolitical issues as a green light for an aggressive move, which Trump may subsequently be compelled to oppose by military force," it adds.
When the property magnate announced his foreign policy team it was also slammed for a lack of experience.