Despite having one year remaining on his contract, the 28-year-old is out of favour and preparing to move on as Riccarton officials trim some surplus from the first-team squad.
The Evening News revealed on Friday that English winger Jordan Roberts will be allowed to leave and Popescu is in the same position.
The centre-back played 23 times last season as Hearts won the Scottish Championship to secure automatic promotion back to the Premiership.
However, this term he has found himself marginalised as a new three-man defensive system remained in place from the end of last term.
He is not likely to feature going forward as John Souttar, Craig Halkett, Stephen Kingsley are established in those three centre-back roles. Peter Haring, Michael Smith and Alex Cochrane can also play there.
Hearts intend to sign a left-sided central defender this month, leaving Popescu with little option but to accept that his long-term future now lies elsewhere.
He will be allowed to depart Tynecastle Park before the summer transfer window closes if another club are willing to take him on.
He joined Hearts last September on a two-year deal from Dinamo Bucharest and previously enjoyed a loan spell with St Mirren in 2019.
Roberts is also preparing to leave Edinburgh in the coming weeks with English clubs interested in taking him back south of the Border.
He has struggled to settle at Hearts and the club will not be difficult to deal with regarding his exit.