HITC Sport understands that the Italy international is poised to make a decision on which Premier League suitor to link up with.
Sources close to the player have confirmed to HITC Sport that the player's demands have also been met by both Premier League clubs, who are hopeful of landing the former Torino star.
Ogbonna is being allowed to leave by the Italian champions, although potential suitors will be paying around £10million to land him.
The 27-year-old has been with Juventus since 2013, when he joined from city rivals Torino, but he has never been able to cement a place in the first-team.
Now he is preparing to head to England, but is deciding whether to move to London or Liverpool.
Roberto Martinez is hopeful he can add Ogbonna to his back-line to challenge both John Stones and Phil Jagielka, whilst new West Ham boss Slaven Bilic sees him as a key recruit and he would likely be lined up to partner Winston Reid in the heart of their defence.
Sources confirmed to HITC Sport that they expect a decision in the next 24 hours, stating: "We should know by the end of Tuesday where he is going."