Cornet overcame Maria 6-3 6-7 (5-7) 6-4 in the second round at Roland Garros on Thursday in a match that ended in acrimony.
The German refused to shake Cornet's hand at the net, instead pointing an accusing finger at her French opponent, who received regular treatment after cramping up during the second-set tie-break.
Treatment for cramping is not permitted in the rules and Maria was doubly angered at the trainer and tournament supervisor, who reacted to Cornet collapsing in pain on the court by helping the world number 50 to her chair.
Maria, who also insisted Cornet exceeded the 20-second rule between points, is unsure what entity she would sue, but told SID: "We want this [legal action] because it was simply not fair in the match.
"I think that's important for the sport. It's not about the defeat. I accept that.
"Even French players have told me that they are behind me. That was nice to hear, because the defeat hurt."