"Constant speculation" refers to ongoing and continuous guessing or assumptions about something without having solid evidence or proof. Full definition
It had felt like a long time coming, with constant speculation over his future. (footballwhispers.com)
Coffee is a commodity just like gas or cotton, so its future value is under constant speculation by commodity traders and coffee buyers alike. (inc.com)
According to the report, Real Madrid head coach Carlo Ancelotti is not out of the picture either if City do decide to part with Pellegrini, but the champions believe he would prefer to remain in Spain despite growing tired with constant speculation about his future. (caughtoffside.com)