According to Borrell, Trump brushed off concerns about the plan's feasibility, claiming that "the Sahara border can't be bigger than our border with Mexico".
"'Just build a wall that borders the Sahara'", he quoted Trump as telling him.
Beyond the sheer size of the Sahara, the other challenge to building such a wall is the fact Spain would need permission to do so from the African countries the massive desert stretches across.
El Pais and Europa Press reported this week that Borrell recalled Trump's suggestion during a luncheon in Madrid on Tuesday.
Building a wall along the US-Mexico border - and getting Mexico to pay for it - was one of the key policies of Trump's presidential campaign.
"While we can confirm that the President has discussed migration challenges with Spanish interlocutors, we do not have record of this specific comment", a senior White House official told CNN.
The conversation between the two politicians is believed to have taken place when Mr Borrell visited the States with the king and queen of Spain in June.
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In June, Trump received worldwide backlash when the U.S. government separated migrating children from parents, some asylum seekers after crossing the border.
They are situated a considerable distance north of the Morocco/Algeria border - across which the Sahara lies.
A spokesman for the Spanish Foreign Ministry confirmed to Borrell's comments to CNN but said the ministry had no further comment in relation to the minister's remarks.
The European country has seen over 30,000 migrants and refugees arrive by sea so far in 2018, making Spain the top destination for migrants arriving via the Mediterranean.
Spain has found itself at the forefront of Europe's migration crisis.
Since the start of 2018, more than 38,000 migrants have arrived in Spain, mostly by sea.
Spain has two small enclaves in North Africa, Melilla and Ceuta, to which migrants do often try to gain entry by way of the those two land borders.