Dolly will not be available for re-homing until they can ascertain whether she has an owner and have sorted her health problems.
Country singer has promised to adopt dog abandoned at Glastonbury, if owner is not found.
A white lurcher was discovered in one of the 5,000 tents discarded at Worthy Farm during clean-up of the festival site last week. She was found cowering in a small and stifling hot tent, clearly distressed, with some food provided but no water in her bowl.
She was taken in by the Happy Landings animal shelter and named Dolly, after the star who stole the show with her debut performance at the event.
In a special video message posted on the BBC News website, Dolly Parton said the she was "very honoured and flattered" that the dog had been named after her.
"I had my manager call the Happy Landings animal shelter to make sure the dog is being treated and cared for properly. At this time, nobody has claimed the dog and the dog is in great hands at the shelter. I will take the dog home to America if nobody claims her within a reasonable amount of time."
Dolly was treated for a serious ear infection and is currently under further assessment. The charity is waiting to see if her owner will come forward, but in the meantime she is living with a member of staff, since their dog accommodation is currently full.
Happy Landings say that they have had many phone calls from concerned members of the public over the last few days, however they stress that Dolly will not be available for re-homing until they can ascertain whether she has an owner and have sorted her health problems.
Contributions to Dolly's ongoing vet costs and upkeep can be made at: http://uk.virginmoneygiving.com/charity-web/charity/finalCharityHomepage.action?charityId=1005992