Elisabeth Kehl of the Voliere Zurich bird protection centre told the NZZ that people were handing over their birds on spurious pretexts.
She said owners were not mentioning bird flu “but the suspiciously high number of cases” in recent days led her to believe this was the real reason they wanted rid of their pets.
The same phenomenon was observed during the last outbreak ten years ago, the paper said.
Kehl said the centre had not come in contact with any cases of bird flu.
Earlier this week Switzerland placed restrictions on the keeping of all domestic and farmed birds as the country steps up measures to stop the spread of H5N8.
Last week Switzerland's federal food safety office (BLV) began monitoring lakes in the country after more than 80 wild birds were found dead around Lake Constance in the northeast.
Infected wild birds have also been found around the lakes of Biel and Geneva in western Switzerland.
The highly contagious virus has only affected wild birds in Switzerland but the fear is it could spread to domestic poultry in the country, after cases were reported on chicken farms in Hungary and Austria.
On Tuesday the BLV said it was stepping up its safety measures and that from Wednesday the whole country would be monitored.
Restrictions will now be placed on all domestic birds living outdoors in order to prevent contact with wild birds, the BLV said in a statement.
There is no evidence the virus can be passed to humans, however the BLV is advising people not to touch dead birds if they find them, and to tell the police.