The law in the Netherlands prohibits the 31-year-old Briton from training with Feyenoord until he receives a work permit, a process which usually takes a week.
Sterling signed for Feyenoord last Thursday, and to get him ready to play as quickly as possible, the club crossed the border to the Belgian football association's training facility at Tubize for sessions on Monday and Tuesday.
"One of the reasons is that Sterling can train with the team," Van Persie told reporters.
"But we can also work on our team culture there. It's for Raheem and for those processes that we're going to do this," he explained.
Feyenoord plan to return to Rotterdam after one more session on Wednesday and hope to have the work permit in time for Sterling to be considered for a debut at home to Telstar on Sunday.
Sterling was a free agent after his contract with Chelsea was terminated last month and signed a contract at Feyenoord until the end of the season.
"My free agent status gave me the opportunity for the first time in a long time to carefully consider the next step in my career," he explained on the Feyenoord website.
"After speaking extensively with (Feyenoord chief executive officer) Dennis (Te Kloese) and (coach) Robin (van Persie), I am convinced that Feyenoord is the place where I will be happy and a valuable member of the squad," he added.
Sterling previously played for Liverpool, Manchester City, Arsenal and Chelsea. He scored 20 goals in 82 international appearances for England.
Feyenoord sit second in the Dutch league, 14 points behind runaway leaders PSV.
Van Persie, in his first full season in charge, was under pressure at the turn of the year when Feyenoord went six matches without a win, but they have won four of six subsequent outings.
