Trump's proposed wall along the US-Mexico border, which spans 3,200 kilometres, could cost up to $20 billion according to some estimates.
Mr Trump won the 2016 USA presidential election partly by promising to build a wall across the 2,000-mile border with Mexico...
"They built this gorgeous wall where the plane went down in Pennsylvania, Shanksville", Trump told the reporters.
The U.S. -Mexico border is approximately 2,000 miles wide.
It was unclear from the Spanish media whether Trump was speaking in jest when he made the purported comments.
Mr Borrell recounted his conversation with the United States president at a lunch event in Madrid this week. Borrell had accompanied Spain's King Felipe VI and Queen Letizia to the White House in June. The UN migration agency reports that more than 33,600 migrants and refugees arrived in Spain by sea so far this year, over 43 per cent of all seafaring migrant arrivals to Europe.
Borrell told his audience that he wasn't in favour of adopting Italy's hardline stance, but said he was concerned about European societies' capacity to absorb a high number of migrants, "especially if they are Muslims".