However, as quickly as the story broke, the buzz surrounding the hypothesised move was dampened by reports that the Bosnian would be offered a new contract with his club, which is currently on top in Serie A, as per Yahoo! Sport.
Pjanic is said to be happy in Rome, and with improved terms on the table, a move for the midfielder could turn into another unsightly chapter in United's already troubled search for an out-of-reach midfield signing.
Rather than attempting to crowbar more settled stars from the clutches of Europe's most competitive teams, David Moyes would do well to consider less obvious targets, such as Inter Milan's Mateo Kovacic.
The 19-year-old Croatian was a target for the club back in 2011 when he was still playing his football at Dinamo Zagreb.
Unfortunately, at the time, the Old Trafford hierarchy were unwilling to sanction the £10 million bid required to secure the services of such a relatively untested starlet, as per Greg Stobart of Goal.com.
Granted, there has so far been nothing to suggest that United are looking again at Kovacic in January, but considering the similar sorts of players purported to be in Moyes' sights, an approach would make sense should other more obvious targets prove to be unavailable.
Having featured for his club and country in a variety of midfield roles, as both a defensive midfielder and attacking playmaker, the teenager is a highly versatile and tactically mature footballer for his age.
In his international debut against Serbia, Croatia's main regional rivals, he was deployed for the very first time as a holding midfielder in Igor Stimac's team and played a pivotal role in his country's 2-0 win, as explained by Zonal Marking's Michael Cox.
This ability to adapt and make unfamiliar assignments work for his team would be extremely valuable in a United squad struggling through transition with an understrength midfield.
Kovacic could be seen as an upgrade to Tom Cleverley, a more dynamic alternative and back-up to Michael Carrick and even an option in the hole.
As well as being an accomplished passer, the Croatian's other main strength is his comfort and confidence in bringing the ball forward on the dribble.
Besides Cleverley, United lack a midfielder with the mobility and technique to drive forward to create movement and pin back opposing defenders and defensive midfielders.
For all their own respective qualities, Marouane Fellaini and Carrick have proven to be ineffective at covering such a role due to their relative lack of pace and more defensive instincts.
Cleverley's usefulness as a quicker link man alongside Fellaini and Carrick has been obvious this season, but as an individual, he is not of the level required to sufficiently influence and dominate games.
Signing Kovacic or another midfielder like him would allow United's two senior midfielders to focus on their specific jobs on the team rather than attempting to broaden their remits and ultimately expose their flaws as all-rounders.
As an upgrade on Cleverley, he would allow the Englishman to be used on a back-up or rotational basis, with United gaining a player able to fulfil the same role in midfield but at a standard more deserving of a regular place in Moyes' starting eleven.
His obvious gifts as a playmaker and dribbler would not prevent him from being able to play in a two-man pivot either, adding some flair to Fellaini's forcefulness or adding a touch of imagination and energy to Carrick's conservative retaining of the ball.
It's unlikely that the Croatian would come cheap with the 2011 valuation of £10 million now needing to be at least doubled, but on the evidence of his performances for his country and tentative appearances for Inter, he could well be worth a major outlay in January.
The rapid acceleration in Paul Pogba's development at Juventus after having been given the responsibility of regular first team football may be painful for United fans to watch, but his emergence also shows what is possible when young stars are handed the spotlight.
For whatever reasons, Pogba was kept at arms length from action in the first team at Old Trafford and yet has proven to be more than capable of playing as a key midfielder for one of Europe's biggest clubs.
Kovacic has made 10 appearances for Inter this year in all competitions, coming off the bench five times, with a few minor injuries curtailing his involvement in Walter Mazzarri's team.
Confusion reigns over his role at the San Siro, however, according to Jeremy Lim of Forza Italian Football, and that could offer any potential suitors a productive angle of approach when it comes to trying to sign him.
Promising to hand Kovacic the vital role of being United's robust and agile playmaker could turn his head towards Manchester and see the youngster blossom in the Premier League just as Pogba has in Turin.
As Adnan Januzaj has already proven this season, if a player is good enough, they're old enough, and with former AC Milan great Zvonimir Boban claiming that Kovacic has the talent to eclipse his own playing career, as reported by James Horncastle for ESPN, the Croat is of the caliber to make an instant impact.
Hailed as the next Luka Modric during his time with Zagreb, he has already been likened to Andrea Pirlo at Inter, according to Marcus Banks of Football.co.uk, and a move to Manchester could see him crowned as the true successor to Paul Scholes.