According to reports in France Football and Le 10 Sport, the French international is wanted by as many as six clubs including United and City.
Barcelona, Paris Saint Germain, Chelsea, Paris Saint Germain and Real Madrid are all heavily linked with the 21-year-old midfielder, who has been valued at between €50m and €60m by Juventus.
The report claims should Pogba decide to leave Turin this summer, his most likely destination would be a return to Manchester. City could be on the lookout for a replacement for Yaya Toure, as the Ivorian international has publicly suggested he could be tempted to leave City.
But United too would also be keen on the midfielder, who famously fell out with Sir Alex Ferguson despite being tipped for the very top at Old Trafford.
Since leaving United in the summer of 2012, the young Frenchman has starred for a Juventus team that has dominated Italian football in recent years.
But with some of the richest clubs in the world interested in his signature, the Serie A champions may find it difficult to resist a big-money offer, especially if it reaches up towards the €60m mark.