Berbatov had been linked with a return to Tottenham, but Press Association Sport understands the Bulgarian has been given permission to speak to Monaco instead.
The 33-year-old is expected to fly to the principality and undergo a medical.
Both parties hope a deal can be concluded before the 2300 transfer deadline.
Berbatov joined Fulham in August 2012 and enjoyed a successful first season with the club, scoring 15 goals.
This term has been a different story for the Bulgarian, however.
He has found the net just four times in the Barclays Premier League and his agent indicated that his client was unhappy at Craven Cottage shortly after the sacking of Martin Jol.
A move back to White Hart Lane, where he was adored by the club's fans, would have been an ideal scenario for Berbatov.
But a transfer to Monaco would still be a good move for the former Manchester United man.
Monaco sit second in Ligue 1 and they have a free space in their starting XI following a season-ending injury to Colombia star Radamel Falcao.
If Fulham clear Berbatov off their wage bill they will have room to bring in new signings.
Tottenham's Lewis Holtby and Greece striker Kostas Mitroglou are two of the most prominent players that have been linked with the west London club, who are second bottom of the Premier League.
The Cottagers also announced on Friday morning that defender Aaron Hughes has joined Sky Bet Championship club QPR on a free transfer.
Hughes told QPR's website: "I don't see this as a drop down in class - I see it as a fresh, new challenge.
"It's a chance for me to come and get some games and help this club build on what's been a good season so far.
"It's a different challenge, but one I'm really looking forward to."
Holtby's agent later confirmed to Press Association Sport that his client had joined Fulham on loan until the end of the season.
"Lewis will stay in London and has joined Fulham on loan until the end of the season," Holtby's agent Marcus Noack said.
The move did not go through without acrimony, though.
Noack accused Tottenham of pricing Holtby out of a permanent transfer back to his native Germany.
"Fulham has put much effort into Lewis," he said.
"It is a very well-run club with an excellent manager Rene Meulensteen. The system and philosophy how Fulham plays fits well with Lewis.
"He will have match practice in the second half of the season in his favourite position and then we'll see how things are going by summer.
"A return to the Bundesliga has been shattered due to circumstances we couldn't control."
Holtby joined Tottenham from Schalke 12 months ago for just £1.25million, but the midfielder's camp claimed Spurs wanted £8-10m for the player.