Kathryn Mayorga claimed via Der Spiegel that the alleged incident took place in a Las Vegas hotel room in 2009 when the Portuguese ace was on holiday.
Ronaldo is alleged to have paid Mayorga £287,000 as an out-of-court settlement to prevent her from making her claims public.
The 33-year-old has strongly denied any involvement, however, and his lawyers will now seek compensation.
"The reporting in Spiegel is blatantly illegal. It violates the personal rights of our client Cristiano Ronaldo in an exceptionally serious way," Professor Dr Christian Schertz said in a statement.
"This is an inadmissible reporting of suspicions in the area of privacy. It would therefore already be unlawful to reproduce this reporting.
"We have been instructed to immediately assert all existing claims under press law against SPIEGEL, in particular, compensation for moral damages in an amount corresponding to the gravity of the infringement, which is probably one of the most serious violations of personal rights in recent years."
Ronaldo joined Juventus from Real Madrid in a £99m transfer during the summer.