The Colombian spent 2014/15 with the Red Devils, but Louis van Gaal’s side opted against making his switch from Monaco a permanent one after he netted just four goals in all competitions.
Despite this below-par return, Chelsea are keen to bring him in, with reports claiming that a £25m deal is close.
The Blues are understood to be favouring a full transfer rather than a loan, with the South American likely to play a back-up role to Diego Costa.
An announcement could be made in the coming few days, with Jose Mourinho looking to bolster his attacking line after guiding his side to the league title.
Falcao was once one of European football’s most feared forwards following prolific spells at Porto and Atletico Madrid, but a serious knee injury suffered while at Monaco has had an adverse effect on his performances.