Not with normal means and abilities
As the question states,the homunculus shares its creator's thoughts, so it would be hard to "get between" the two with mundane persuasion, etc.
From the MM p.88, Homunculus entry, Shared Mind. ability:
A homunculus knowns everything its creator knows...Everything the construct senses is known to its master, even over great distances, provided both are on the same plane.
A shared mind and mystical bond aren't things that can easily be subverted with a little deception.
Not with common spells
Even spells like Dominate Monster don't work, as they rely on the charmed condition:
While the creature is charmed [you can] issue commands (PH)
Trickery while they are on Different Planes
Tricking it while its mentally separated from its master by being on a different plane may be possible. (A homunculus has an Intelligence and Wisdom of 10 each, so deceiving it is quite possible.) Perhaps this could most easily happen if the creator or homunculus were in a demiplane created by Rope Trick or a similar spell or magic item.
Possibly with Madness
If madness were inflicted upon the homunculus and/or its owner, the homunculus might "attack the nearest creature" or "do whatever anyone tells him or her to do that isn't obviously self-destructive" (DMG p.259, Madness Effects)
Demons can inflict other violent forms of madness, as described in Out of the Abyss.