Feyenoord fullback Karsdorp, 22, arrived in Rome on Tuesday morning and "will have a medical in the Italian capital, ahead of a proposed move to the Giallorossi from current club Feyenoord," Roma said in a statement.
Roma, who have secured an automatic spot in the Champions League, are hoping to strengthen for a fresh assault on the competition next season.
However, the capital club, who will be coached by former Sassuolo coach Eusebio Di Francesco, have several transfer issues to resolve.
New club sporting director Monchi recently oversaw the sale of speedy Egyptian winger Mohamed Salah to Liverpool for a reported €39 million ($43.5 million).
He is also reported to have agreed to sell Greek defender Kostas Manolas to Zenit Saint Petersburg.