Pirlo's future at current club Juventus is in doubt as some reports have suggested that current Juve boss Antonio Conte will not offer the veteran a new deal.
And, Red Devils boss David Moyes could make a move to bring him to Old Trafford as a short-term replacement for recently retired Paul Scholes.
The 34-year-old's contract runs out at the end of the season, meaning he could join the Premier League champions on a free.
However, United will have to convince him to join them over their Premier League rivals, as Chelsea, Arsenal and Tottenham are all monitoring the situation.
Pirlo, who has helped Juventus secure back-to-back Serie A titles, could also become a target of Spanish giants Real Madrid, with Carlo Ancelotti a well known admirer.