Falcao was hoping to resurrect his ailing career at Chelsea this year, but halfway through a season-long loan with the Premier League champions, the Colombian has scored just one goal.
The 29-year-old has not played for Chelsea since the end of October due to a thigh injury and is expected to be out for at least another week with the problem.
Falcao was at Monaco's training ground earlier this week for checks on the injury.
The striker returned to Chelsea's training ground on Wednesday and was at the the complex in Cobham on Thursday too.
But he is understood to be considering an attempt to cut his loan short and return to Monaco
With Diego Costa and Loic Remy ahead of him in the pecking order, Falcao appears unlikely to get much playing time with the Blues for the rest of the season, which is of concern to the former Atletico Madrid forward.
If Chelsea cannot offer him regular first-team football for the rest of the campaign, it is understood the Colombian would prefer to return to Monaco.
Press Association Sport understands Falcao has recently rejected approaches from Mexican and Turkish clubs.
Falcao's contract with Monaco expires in 2018
Monaco signed the striker from Atletico in 2013 for £52million, but he spent just one season in Ligue 1, suffering a major knee injury midway through, before embarking on a disappointing loan spell at Manchester United in which he scored just four goals in 29 appearances.
Prior to his time in England, Falcao was regarded as one of the best strikers in the world following prolific spells at Atletico, Porto and River Plate.
Source : PA
Source: PA