The 20-year-old defender has emerged as a top target for the Bianconeri in recent times.
An aging backline is in need of reinforcement and those in Turin are starting to piece together plans for the future.
They have already seen Medhi Benatia depart, with the Morocco international having completed a January switch to Qatari side Al-Duhail.
Giorgio Chiellini and Leonardo Bonucci still have plenty of football left in them, but they cannot go on forever.
With that in mind, Juve are looking to ensure that they have suitable successors in place, with Romero fitting the mould as he prepares to finalise a switch to the Allianz Stadium.
Genoa had been hoping to generate around €35m (£31m/$40m) from any sale, but a deal which includes a number of bonuses could see a compromise reached.
Once an agreement is pushed through, Juve will then take a decision on what do with Romero in the immediate future.
He will officially join their books during the summer transfer window, but may not figure for them in 2019-20.
One option being considered is to allow the youngster to spend next season back on loan at Genoa.
The highly-rated Argentine will then be given a chance to see regular game time while furthering his development.
That may be the best option as Juve are also exploring the possibility to luring Matthijs de Ligt away from Ajax.
If Juve were to win the race for the Netherlands international, he would slot straight into the first-team fold at the club, meaning regular opportunities for Romero would be limited.
De Ligt is only 19 years of age, but is considered to be a ready-made option for anyone prepared to pay the going rate for a player of his obvious potential.
Romero, meanwhile, only linked up with Genoa in the summer of 2018 after departing Belgrano in his homeland, but is considered one of the top young defenders in Serie A.
Fourteen appearances have been taken in during his time in Italy, with one goal recorded, and his rapid rise to prominence is what has brought him to the attention of league champions Juve.