The Chelsea forward was not part of Gareth Southgate's squad as they beat the African champions Senegal 3-0 on Sunday to set-up a quarter-final clash with France.
Sterling's absence is understood to have followed a break-in at his house on Saturday evening, leaving the England international understandably shaken and concerned about the well-being of his children.
When asked if he thought the 27-year-old would figure at the tournament from here, manager Southgate said on ITV1: "We've got to wait and see.
"At the moment clearly the priority is for him to be with his family, and we're going to support that and we're going leave him to have as much time as he needs. He's going home."
He added: "I really don't know (the likelihood of him returning) because at the moment it's a situation that he needs time with his family and I don't want to put him under any pressure with that.
"Sometimes football isn't the most important thing and family should come first."