The Colombia international, on a season-long from Monaco, was reportedly in the Spanish capital on Monday in the hope of sealing a return to La Liga.
However, those hopes were ended when a move to China fell through for Atletico's Jackson Martinez.
Falcao has made just one Premier League start for Chelsea and his only goal in 15 appearances came as a substitute.
Media playback is not supported on this device
The 29-year-old arrived at Stamford Bridge last July having had a disappointing loan spell at Manchester United during the 2014-15 season.
He has not played for Chelsea since 31 October, was sidelined with a thigh injury at the start of November and suffered a recurrence of the problem in a training game in December.
During two years at Atletico, Falcao helped the side win the 2012 Europa League and 2013 Copa del Rey.
He scored 52 goals in 68 league games for the Colchoneros.

The 26-year-old, who has not featured for Sunderland this season, could make his debut for the Championship side against QPR on Saturday.
The former Chelsea trainee is the first player to join Leeds since Steve Evans was appointed head coach last month.
Meanwhile, the Black Cats have recalled winger Will Buckley, 26, from his loan spell with the Elland Road side.
Buckley joined the club on a three-month loan in October, but has not played in any of the club's last four matches.

People will be brought to shore from a "shipwreck" via breeches buoy by members of the South Shields Volunteer Life Brigade in a re-enactment of a rescue on 2 April 1866.
A seine-net fishing boat will play the part of the schooner Tenterden which was wrecked during a heavy storm.
The event, near the watch House off the South Pier, is part of the brigade's 150th anniversary celebrations.
Over the weekend there will also be a special dinner, and a Service of Thanksgiving in St. Hilda's Church on Sunday.
A breeches buoy is a lifebuoy with a canvas sling - similar in form to a pair of breeches - attached to a rope and pulley. The rope is fired on to the vessel by a rocket.
At the time of the rescue, the brigade had only been in existence for two months, and although there had been three practice drills it was the first time the equipment had been used in a life-or-death situation.
Despite the bad weather, all those on board the ship - including the captain's wife and their 18-month-old baby, were winched to safety.
The men were taken to a nearby public house, while the woman and child were tended to by local women.
South Shields Volunteer Life Brigade is credited to have saved more than 600 lives from shipwreck since it was founded, and has now branched out into search and rescue operations.
As part of the anniversary celebrations there will be a series of illustrated talks and open days, and later in the year a major exhibition in South Shields Museum.
Chelsea striker Radamel Falcao was denied the chance to re-join Atletico Madrid on transfer deadline day.
[NEXT_CONCEPT]
Leeds United have signed Sunderland midfielder Liam Bridcutt on loan until the start of January.
[NEXT_CONCEPT]
A sea to land rescue is set to take place on the South Tyneside coast.