As of Tuesday afternoon, Anastasia Potapova agreed to compete under a neutral flag in order to play in her first round match in the Monterrey Open.
Svitolina, who is the tournament's top seed, released a statement on Monday revealing that she would take no further part unless her opponent dropped all affiliations with Russia.
The WTA are yet to comment on the situation, but ahead of the match Svitolina said, "There's been a lot of discussion.
"Today they will release a statement that they will remove the flags. So we are waiting just for the final confirmation about that. I will be playing tonight because my opponent is going to be under a neutral flag."
Svitolina went on to criticise a lack of action from tennis' governing bodies, stating more has to be done to sanction Russia and Belarus following an invasion of her home country.
"In the tennis community, more should have been done.Today is already six days that serious and horrible things are happening in Ukraine.
"That's why I decided to make a move because I didn't feel enough support from our tennis community. As Ukrainians, we couldn't sit silent anymore in feeling so much pain."
Potapova was happy to play under neutral terms, but added that she as a professional athlete feels like a "hostage" due to the ongoing conflict.
In the 20-year-old's Instagram post, she said "Unfortunately, now we, professional athletes, are becoming hostages of the current situation.
"I'm sorry, but even though I am a stranger to politics, I am against grief, tears and war."
The match is scheduled to start at 01:00 GMT in Mexico, and world No.15 Svitolina has confirmed that she'll wear the colours of Ukraine during the match.
The 27-year-old added: "For sure it's not going to be another WTA match. I feel like I have my country on my shoulders."