Mr Trump will travel to Laredo, Texas, on Thursday to meet border control agents and local police officers, according to his campaign office.
In June, he sparked controversy after calling undocumented Mexican immigrants "rapists" and "criminals".
Some recent polls put him top of a crowded field of Republican candidates.
But most of them were conducted before Mr Trump's comments on Senator John McCain's military record, in which he questioned the veteran Republican's "war hero" status because he was captured.
The attack was widely condemned and his rivals, who are increasingly frustrated by him dominating media coverage, hope it could damage his standing.
Mr Trump was invited to the Mexican border by the Laredo group of the National Border Patrol Council earlier this month.
Hector Garza, president of Laredo border agents, told reporters he was looking forward to giving Mr Trump "a boots on the ground perspective".
Earlier this week, the outspoken businessman received heavy criticism after giving out the mobile phone number of a rival at a campaign rally.
Mr Trump told supporters Senator Lindsey Graham was an "idiot" and told his supporters to call the number.
It followed Senator Graham denouncing Mr Trump as "a jackass" after condemning the real estate mogul's comments about John McCain.
On Wednesday, Republican favourite Jeb Bush criticised Mr Trump's rhetoric on immigration and his comments on Mr McCain but said his supporters had "legitimate concerns".
"I respect the sentiments people feel when they hear Trump talk," he said at a campaign event.
"The problem with Mr Trump's language is that it's divisive, it's ugly, it's mean-spirited. We have to separate him from the people that have legitimate concerns about the country," he added.
Meet all of the 2016 hopefuls
US presidential candidate Donald Trump is to visit the border with Mexico after making illegal immigration the centrepiece of his campaign.