The little-known designer Norisol Ferrari worked with Trump because she does not believe in discrimination in any form.
Market sources say Versace is working on an expansion plan ahead of the listing and that its has recently held discussions with Tisci.
The designer is to show his debut collection for the French house in Paris.
Founders Mikael Söderlindh and Viktor Tell will remain involved with the company.
The two firms still have to execute a merger agreement.
The fund purchased a 70 percent stake in the French shirtmaker from EPI group.
The beauty giant is purchasing CeraVe, AcneFree and Ambi from Valeant.
The deal would cost as much as 19.8 Hong Kong dollars, or $2.6 billion. Intime operates 29 department stores and 17 shopping malls, mainly in first- and second-tier cities in China.
Investment bank Moelis & Co. is reportedly advising the Singapore-based private equity arm on a deal to buy the brand from Billabong International.
Clessidra and the Buccellati family will retain a 15 percent stake in the company.