Cops nabbed the pervert who allegedly broke into a girl’s home in Manhattan and molested the 10-year-old while she was sleeping, police said Thursday.

Raymond Wilson, a 31-year-old homeless man, is accused of sneaking into the girl’s Noho apartment near Broadway and Bond Street early on June 12 and rubbing his crotch on her feet, cops said.

Wilson took off when the child woke up, police said.

Cops arrested Wilson on Wednesday and charged him with sexually motivated burglary, sex abuse, grand larceny and acting in a manner injurious to a child less than 17 years old, police said.