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The 16-time Grand Slam winner, who lost in the last eight last year following four straight final appearances, faces Djokovic after the second seed's scheduled quarter-final opponent, Italy's Fabio Fognini, withdrew through injury.
"He (Monfils) is a superb player, so I knew the danger of this quarter-final," said Federer after his sixth career victory over Monfils.
"I'm very happy to be in the semi-finals."
Former world No 1 Federer, the 2009 champion, has made steady progress in the tournament to date and is yet to lose a set.
Djokovic, however, has beaten the great Swiss in their three previous encounters and requires just one more victory to level John McEnroe's 1984 record of 42 matches unbeaten at the start of a season.
A victory on Friday will also crown the Serb as the new world No 1.
"Playing a semi-final here at Roland Garros is a great moment and playing such a great player is what we train for," added Federer.
Federer made an uncertain start amid windy, overcast conditions on Court Philippe Chatrier and was broken to love in his second service game.
The Swiss broke back immediately, however, thanks to a perfectly judged backhand drop shot that bit and died in the dust, before obliging the ninth-seeded Monfils to fight off three break points in the eighth game.
Seeded outside the top two at a Grand Slam for the first time since Wimbledon in 2003, Federer brought up two set points on Monfils' serve shortly afterwards and then clinched the first set when the world No 9 put a forehand wide.
Following an exchange of breaks in the second set, Federer broke for a 4-2 lead when Monfils double-faulted, prompting the Frenchman to fling his racquet to the ground in disgust.
Both men were culpable of some dismal shot-making, but it did not prevent Federer from closing out the set when a stretching Monfils sent a backhand long.
Monfils saved three break points at 4-4 in the third set and two at 5-5, but swiftly fell 6-1 down in the ensuing tie-break and was finally beaten when Federer thrashed a forehand winner down the line.
Results Roland Garros on Tuesday (x denotes seeded player):
Men
Quarter-finals
Roger Federer (SWI x3) bt Gael Monfils (FRA x9) 6-4, 6-3, 7-6 (7/3)
Novak Djokovic (SRB x2) bt Fabio Fognini (ITA) - walkover
Fourth Round
Andy Murray (GBR x4) bt Victor Troicki (SRB x15) 4-6, 4-6, 6-3, 6-2, 7-5
Women
Quarter-finals
Marion Bartoli (FRA x11) bt Svetlana Kuznetsova (RUS x13) 7-6 (7/4), 6-4
Francesca Schiavone (ITA x5) bt Anastasia Pavlyuchenkova (RUS x14) 1-6, 7-5, 7-5
