The phrase "baseless rumour" means a piece of information or gossip that has no evidence or truth behind it. It is something people talk about without any real facts to support it. Full definition
I I do nt expect an article on daily baseless rumours on this site. (justarsenal.com)
They are spreading baseless rumours about Boris Johnson and Michael Gove reneging on their campaign promises. (thesun.co.uk)
Donnarumma was seen being consoled by Leonardo Bonucci in the dressing room and on the pitch while Gennaro Gattuso and sporting director Massimiliano Mirabelli rallied around him and insisted that he had not suggested he wanted to leave, which would lead us to believe that baseless rumours have sparked an unnecessary reaction from a small section of supporters. (caughtoffside.com)