The store owners say they didn't see her that night she claimed to go buy a soda.
Flyers have been posted around her town of Jersey City asking for the public's help in locating Velasquez.
"Her children are thinking that she went to go give birth. They are wondering why she's not here, cause it doesn't take that long to give birth," said Velasquez's mother.
Family members say the native of Puerto Rico is the mother of two girls, ages 5 and 9.
Her boyfriend, who is the father of the children, lives in Puerto Rico. Family members said Friday that she planned to visit him soon.
All police are saying it they have a person of interest they want to speak to.
Anyone with information on Aileen Velasquez's whereabouts is asked to call police.
(Information from WABC-TV and The Associated Press).