The Dutch attacking midfielder, formerly of Liverpool, has agreed terms on a three-year deal with the Istanbul club after spending just one season back at boyhood club Ajax
The Dutch winger will be leaving Ajax after a one-year stay at his boyhood club, having signed for the Amsterdam giants from Hoffenheim last summer.
The likes of Real Betis had been linked with his signature but the Turkish club look set to seal a deal for the 26-year-old.
"We have agreed to everything with Babel. We will sign a three-year deal with him," Erkan told Radyospor.
Babel started his career with Ajax before winning a move to Liverpool in 2007. His form at Anfield stagnated, however, and he moved to Hoffenheim in 2011.
After just 18 months in Germany, he returned to the Dutch capital last summer and scored four goals in 16 appearances in an injury-ridden season back in the Eredivisie.
Kasimpasa, meanwhile, performed well in the Super Lig last season, finishing sixth and missing out on a Europa League spot by just five points.