"There's" (there has) is perfectly appropriate.
“There’s”
‘There’s” (there has) is perfectly appropriate.’
It doesn’t work in this case because the verb needs to agree with “stories”, which is plural. (I.e.: “There’s been stories”) You can see the issue by rearranging the structure, but keeping the same noun & verbs:
Stories has been going around [verb/noun disagreement]
Stories have been going around [verb/noun agreement]