Josep Borrell said the United States president dismissed any doubts expressed by Spanish diplomats, who pointed out that the desert stretched for 3,000 miles.
Spanish officials expressed skepticism and reminded Trump of the vastness of the Sahara, El Pais reported Borrell as saying, but Trump is said to have brushed off their concerns and quipped, "The Sahara border can't be bigger than ours with Mexico".
The US-Mexico border is a little under 2,000 miles long.
It would be similar to Trump's planned wall across the US-Mexico border to stop illegal immigration. Some parents were sent to jail while their children were held in foster care as "unaccompanied minors".
In this Wednesday, May 9, 2018 photo provided by Liberian Ju Dennis, fellow migrants being expelled from Algeria lie in a truck headed towards the Niger border at Point Zero, from which they must walk south into the Sahara Desert towards the Nigerien border post of Assamaka.
Fans and worldwide media wondered how the U.S. would manage the issue of borders as a host of the 2026 World Cup.
Spain has seen rising numbers of migrants and refugees arrive on its shores in recent months, the result of a crackdown on a central Mediterranean route between Libya and Italy. Out of those, 33,611 came through Spain.
Spain has outpaced, according to the report, Italy and Greec, with over 43 percent of all undocumented migrations from the Mediterranean in 2018.
However, if Spain was to build a wall as suggested by Mr Trump, it would be complicated by the fact that it would have to be built on foreign territory.