It may seem an unusual approach, but the family has so far preferred to wait for interest to develop naturally rather than push for a move once Vlahovic becomes available on a free transfer from Juventus.
That stance could change if an agreement is reached between the forward and the Bianconeri, with new sporting director Giovanni Carnevali having decided to reopen talks over a possible renewal.
Had previous sporting director Damien Comolli remained in his post, sources suggest there would have been no fresh attempt to keep the striker, but a shift in approach, partly driven by financial considerations, has reopened the possibility.
Any renewal would not come close to the figures previously sought by Vlahovic's camp, which would have amounted to roughly 30 million euros between gross commissions and a signing bonus.
Those demands made an agreement difficult to reach, though transfer valuations can shift quickly in this market, as was shown by Lois Openda's situation last summer.
The fact that no other club has yet made concrete contact works in Juventus's favour, with no major offers currently on the table for the Serbian forward.
That picture could shift in the coming weeks, although the ongoing World Cup is having a noticeable dampening effect on transfer activity across the market.
Vlahovic's situation remains one of the more closely watched sagas of the Italian transfer window, with his contract status adding pressure on both sides to reach a resolution before he becomes free to discuss terms with any interested club.