The 23-year-old attended a CAS hearing in Switzerland last month and the court will reveal its verdict at 1630 GMT on Thursday.
Gasquet has previously said that the drug got into his system after he kissed the woman in a nightclub in Miami.
The tribunal supported his claim and felt that because "no more than a grain of salt
" was recorded in the sample a long ban would have been an injustice.
He is obviouly not using if that is all that was found in his system. if he is banned for 2 years, it will be disgraceful IMO to wreck someone's career for that long.