Caicedo joined the Seagulls from Independiente del Valle for £4.5m in 2021 and has become an integral part of Roberto De Zerbi’s squad.
The midfielder has two-and-a-half years remaining on his current deal and it is understood the south coast club are reluctant to let the 21-year-old leave without a succession plan in place.
Arsenal are reportedly considering their options and could go back with a revised offer.
Chelsea are also interested in the player after signing Marc Cucurella from Brighton for £57m at the start of the season, but the clubs are "not in the same ball park" in terms of valuations, according to Sky Sports.
The Gunners remain in pole position to sign West Ham midfielder Declan Rice in the summer whether or not they sign Caicedo.
Speaking ahead of their FA Cup match against Liverpool, De Zerbi told reporters: "Moises is a good guy, he's focussed only on us. He's relaxed. I hope he stays with us until at least the end of the season.
"I spoke with Moises and told him it's difficult to change during the season. I spoke to him as a father, not a coach."
