The 33-year-old was suspended for 30 days last Wednesday for what the U.S. Soccer Federation called "an incident that occurred during the current WNT training camp" in Carson, California.
Asked whether she could be omitted from the team's World Cup roster, USSF President Sunil Gulati said Monday: "Look, that's possible. We hope that's not the case. We hope she's making progress and joins the team. That's certainly the goal, hers and ours."
Jerramy Stevens, Solo's husband, was driving a team vehicle when he was arrested last week on suspicion of driving under the influence, a person familiar with the details of the arrest told The Associated Press last week. The person spoke to The Associated Press on the condition of anonymity because they could not discuss the case publicly.
Solo was ordered to refrain from drinking alcohol last June after she was arrested on domestic violence charges at her sister's home in Kirkland, Washington. The charge was dropped this month.
Speaking on a conference call with U.S. coach Jill Ellis, Gulati said he had to speak carefully because of the involvement of "health-related issues." Asked whether Solo had been asked to undergo alcohol counselling, Gulati said "I think neither of us denied or confirmed that."
"She's been given time to deal with some issues, and we think that in this period she'll certainly start that process, and we'll evaluate," he said.
Gulati said the length of the suspension was determined during conversations he had with Ellis and USSF Secretary General Dan Flynn.
"Thirty days seemed to be the appropriate suspension under our rules and given the circumstances," he said. "So there are a number of things that Hope is being asked to do in that 30 days. We're not going to get into the specifics of that. And then we'll evaluate where things stand at the end of that period and make the decision going forward."
Solo will miss exhibition games at France (Feb. 8) and at England (Feb. 13). She could return for the Algarve Cup tournament in Portugal in March.
"The situation warranted a consequence, and we thought it was reasonable," Ellis said. "This is important for us to be able to focus the players that we have on these games and then allow Hope some time to sort of reflect on some things. So I think as far as the specifics, like Sunil said, we're not going to get into those, but Hope and I had some very good conversations and I'm optimistic about moving forward."
Ellis said forward Alex Morgan was "fully integrated back into this training camp" reinjuring her left ankle Oct. 17 during a game against Guatemala at the CONCACAF Women's Championship. Morgan, who has 49 goals in 77 international appearances, was sidelined for seven months after injuring the same ankle during training in October 2013.
"She's coming along great. We're very excited about where she is," Ellis said.