"possess influence" is a correct and usable phrase in written English.
You can use it to refer to someone or something that has the power to exert an effect or have an influence over someone or something else. For example, "He has long possessed influence over the local business community."
The players possess enormous influence.
Few billionaire investors possess the influence of Warren E. Buffett, chief executive of Berkshire Hathaway.
The adoration or morbid curiosity vested in them seems misplaced to many; although few would question the fact they possess an influence of a kind that politicians spend millions of pounds and hours attempting to attain.
He said he thought that Islamic clerics drew their authority from their followers as well as from God, and that while they should possess wide influence, they should not govern directly.
The district governor wielded his connections to Kabul as best he could, but did not possess great influence, in part because — in keeping with the most sophisticated state-building methods — government aid was mainly distributed by locally elected committees.
How he came to possess that influence — and irrevocably change the course of Italian politics and culture — is the subject of "The Sack of Rome," an illuminating new book by the journalist Alexander Stille, one of the best English-language writers on Italy.
Traditional chieftains possess great influence on indigenes and tend to rein in dissenting or 'rogue' community members.
The adhesive modulus is another factor that has been reported to possess considerable influence on the shear stress.
For example, Martin Luther King Jr.'s quote: "Injustice anywhere is a threat to justice everywhere". Companies like Google possess the influence of a million MLKs.
Uttal et al. 1992argue that many CTOs believe that both they, and technologies, in general, are undervalued by their organizations and that they do not possess enough influence in their organizations.
