The Serbian arrived at Manchester United once before, but didn’t stick around for too long even as the club had confirmed he would join from Partizan Belgrade.
After regularly training with the Red Devils throughout 2009, purported issues securing a work permit would see his move scheduled for the following year collapse.
Instead, Ljajic would depart his homeland for Fiorentina, cutting his teeth at the Stadio Franchi before being called in as a replacement for Erik Lamela at Roma in August - for a fee in the region of €11 million.
However an auspicious start in the Italian capital - the versatile forward netted just 14 minutes into his Giallorossi debut - has given way to a fair bit of frustration with his new employers.
The rise of Gervinho and conversion of Alessandro Florenzi to a winger by boss Rudi Garcia has seen space limited for Ljajic, who has started just 12 Serie A games this season.
There has been the occasional flash of brilliance, but the 22-year-old has hit just two goals since September and for the most part has cut an exasperated figure.
Gazzetta dello Sport have now claimed that Roma aren’t opposed to offloading the youngster come June as Garcia hasn’t been entirely convinced by his displays.
So could United re-enter the frame for their former target?
Yet the central question is, where would Ljajic fit in?
The Serbian is able to play nearly anywhere in attack and could occupy any of the front four spots for Moyes, though is most comfortable on the left in a supporting role.
An issue is that United already have a log jam in this area, however - the latest headache coming in the form of how to fit both Wayne Rooney and Juan Mata in simultaneously.
But if Moyes does trim his squad before making any new signings, for instance jettisoning Ashley Young, and can find clearly defined role for Ljajic - even if off the bench - there may be a place for him at Old Trafford.
That is, as long as United are willing to shell out the cash Roma would hypothetically demand, having paid an initial €11m to take him on.
Ljajic was close to United once, and if Roma are indeed serious about listening to any proposals for him, it’s not entirely out of the realm of possibility the sputtering champions could have another look.