The Colombia international has endured a difficult start to life at Old Trafford following his season-long loan move from Monaco in September.
After being ruled out for much of last season due to a cruciate ligament injury, Falcao was thought to be around two weeks away from a return due to a calf complaint picked up in training.
United boss Louis van Gaal said on Saturday that Falcao would not be considered for a starting place until proving his fitness, but the former Atletico Madrid man took to Twitter on Sunday to declare himself ready for selection.
"Back to training 100 per cent and ready to help the team in the next games," Falcao said.
Falcao has scored one goal in five league appearances for United so far this season.
Van Gaal's men host Hull City in the Premier League on Saturday.
