10:45 AM PT -- Kelly's attorney in Monaco tells us the Daily Mail report is not accurate.
Giersch had been granted full custody during a hearing, but court sources say Kelly's appeal is expected to be heard later this week.
Kelly Rutherford's kids will not return to their native U.S.A -- a judge reportedly granted full custody to Kelly's ex-husband Daniel Giersch, who now lives in Monaco.
The ruling in a Monaco court is a devastating loss for the "Gossip Girl" star, who's been battling Giersch for years over 9-year-old Hermes and 6-year-old Helena. According to the Daily Mail ... the judge said the exes must make joint decisions regarding the children's schooling, education, and housing.
However, Kelly will only be allowed to visit in Monaco or France.
The children -- who are U.S born citizens -- were last in this country during the summer. Kelly was devastated after an August hearing though that sent them back to Daniel in Monaco, and they've been there ever since.