The Colombian had initially been named in the Monaco squad but was withdrawn from the matchday list at the last minute amid mounting speculation that he is on his way out of the principality club.
Real Madrid, Juventus and Manchester City have all been closely linked with a move for the 28-year-old, who on Saturday evening did little to quell the speculation by posting a tweet which read: “Dream come true #HalaMadrid”.
The tweet, including a slogan used by Real Madrid fans, suggested that Falcao was bound for the Santiago Bernabeu, although the player deleted it shortly afterwards and then claimed that the message was faked.
“I have to deny a report about a tweet that I did not do and that was photo-shopped,” he wrote.
Falcao started and scored the winning goal, his second of the season, last weekend against Nantes and had been expected to start for Leonardo Jardim’s team against Lille at the Stade Louis II.
In his absence, Dimitar Berbatov started and scored as Monaco drew 1-1, a result which leaves them with just one win and four points from their first four Ligue 1 games.
Falcao, wearing a Monaco club suit, watched the game from the stands next to his agent Jorge Mendes and club vice-president Vadim Vasilyev.
When asked about the striker’s absence, Monaco coach Leonardo Jardim said: “Falcao was unavailable. I can’t say any more than that. I don’t know if he is going to leave and I don’t want to talk any more about it.
“I really like Falcao but the most important thing is to talk about the match.”
The former Atletico Madrid striker moved to Monaco for a fee in the region of 60 million euros ($78.8m, £47.5m) last summer but his season was ended by a serious knee injury suffered in a French Cup tie in January that also ruled him out of the World Cup.
Falcao, who has scored 13 goals in 22 appearances for the principality club, could follow the path taken by his compatriot James Rodriguez, who left Monaco for Real Madrid in July.
However, any move will have to be completed before the summer transfer window closes on Monday.