The Portugal defender joined Juve in January on-loan from Chelsea, though without a permanent option.
It had been previously suggested Juve had chosen to send Veiga back to London at the end of the season.
However, Tuttosport is reporting today that Juve now want to explore keeping hold of the young defender.
Chelsea boss Enzo Maresca regards Veiga highly, but the decision to keep hold of him could be taken out of the manager's hands.
Juve have been informed it will take €50m to buy Veiga this summer, though there is hope at their end that the initial price can be negotiated down. Juve paid €4m (plus €1.5m in bonuses tied to achieving certain objectives) for the six-month temporary deal.