The 21-year-old has been a key part of the Seagulls side who finished sixth in the Premier League this term, earning the club their first-ever berth in European football.
Having featured 30 times already for Ecuador - including at last year's World Cup in Qatar - the midfielder has attracted a lot of interest with his performances since returning from a loan spell at Beerschot in Belgium.
According to The Mirror, Mikel Arteta's Arsenal have agreed personal terms with Caicedo ahead of a potential move to the Emirates, with Premier League rivals Chelsea and Liverpool also interested in the player.
It is believed that the Gunners' success in qualifying for the Champions League next term means that they now lead the race for Caicedo's signature, with the Blues and Jurgen Klopp's Reds both missing out on a place in Europe's elite club competition.
The report claims that Roberto De Zebri's men are demanding a transfer fee in the region of £75m for one of their star players - the fact that the Ecuadorian signed a new contract at the start of this year puts the Seagulls in the position to command a sizeable fee.