Spain also has no border with the Sahara, meaning it would have to build the barrier on foreign land.
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.
Trump's call for a wall on the southern border - which he repeatedly insisted that Mexico would pay for - was a hallmark of his presidential campaign, with "Build the Wall!" chants still breaking out at his frequent "MAGA" rallies.
2 patients drown as van swept into floodwaters
Richardson says the women were being transported from a hospital in Horry County to medical facilities in Florence and Darlington. SLED , the South Carolina Highway Patrol and the Horry County Sheriff's Office are investigating the incident.
"The border with the Sahara can not be bigger than ours with Mexico", the president reportedly told Mr Borrell.
Mr Borrell told the story at a lunch event in Madrid this week, in comments that were widely reported by the Spanish media.
Since the start of 2018, more than 38,000 migrants have arrived in Spain, mostly by sea.
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".