The animal, described as being about 50cm tall with black fur and a long tail, was first spotted last Wednesday in the Kestenholz-Bätterkinden region. Since then, it has been seen twice more, including once by a game warden, online news site Blick reported.
Although the animal has not been confirmed as a panther, police said that the description seemed to fit the bill.
"The police have set up several photo and bait traps. These are now being evaluated," Melanie Schmid from the Solothurn police told the website.
Search parties have not gone in to the woods because it is thought that the creature is shy. Until the animal has been identified, no safety warnings will be issued to hikers by the police.
Once located, police plan to stun the animal and take it into captivity.
The origin of the creature is unknown. Police have contacted all possible owners of panthers in Switzerland, including zoos, circuses and private owners, but none have reported a missing animal. This has led police to conclude that the beast may have been taken into the country illegally.
The black panther is not in fact its own species, but rather an all-black version of one of the other big cats, most commonly leopards or jaguars. Many of these big cats have excessive melanin pigmentation in their fur, which is why they appear black, although on close inspection, typical markings can often be made out.