Verratti limped off during a game against Guingamp last month and was diagnosed with a sprained ankle, making him a doubt for the last-16 tie against United.
But the Italy midfielder trained with his team-mates on Monday and could be fit to play at Old Trafford on February 12.
Thomas Tuchel is expected to be without Brazil forward Neymar for both legs, however.
Verratti was absent as PSG lost for the first time in Ligue 1 this season, falling to a 2-1 defeat away to Lyon on Sunday.
The midfielder has featured in 14 Ligue 1 contests this season, as well as five of PSG's six Champions League matches to date. He has managed just an assist in the two competitions.
Despite that setback against Lyon, PSG are coasting in Ligue 1 and with a 10 point advantage over second-placed Lille, and two games in hand on their nearest chaster, look set to take home yet another domestic honor.
However, it in the Champions League where Thomas Tuchel will be looking to overturn recent history and take the club to new heights in the competition.
PSG's recent spell of domestic success have still seen them limited to just the quarterfinals in the Champions League, and the last two seasons have seen the club go out at the round of 16 stage of the competition.