The Seagulls are defiantly standing by their position that the Ecuadorian, 21, is not for sale in the January transfer window.
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Brighton boss Roberto De Zerbi revealed on Sunday that Caicedo could depart before Tuesday’s deadline.
But Sky Sports have now claimed a fresh £70m offer from the Gunners has failed to persuade the south-coast side to sell.
And it is thought that Brighton’s position will not change before the window closes.
Caicedo has been told to stay away from training until after the deadline passes and was excluded from Brighton’s FA Cup win over Liverpool at the weekend.
It comes after he pleaded with the club to let him go in a social media post on Friday – following Brighton’s decision to reject a £60m bid from Arsenal.
Speaking after the Seagulls’ fourth round victory in the FA Cup, De Zerbi told ITV: “Moises is a good guy. We will see tomorrow and the next days what happens.
“We hope he stays with us for the rest of the season, but this is a question for the club and Moises.
“Moises is a good guy. In life you can make mistakes. We will see the best solution for the club, for him and for us.”
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He then went on to add: “Caicedo is a very, very good guy.
“I can understand him because when you are 21, and you receive the request of a big, big team that are playing in Europe, I can understand.
“I would like that he can finish the season with us but we are ready to go forward without him.”
De Zerbi then admitted that losing Caicedo in the January window would be a major blow to his squad.
And given they have already seen Leandro Trossard depart to Arsenal, the Italian believes they would need to bring players in to fill the void before the window closes.
“We lost Trossard, if we lose also Caicedo it can be a problem for us,” he said. “If we want to fight for Europe, or the maximum on the table.
“If we want to stay like this (at our current level), we can. But I don’t like.”
Caicedo joined Brighton from Ecuadorian side Independiente two years ago for just £5m.
He has contributed two goals and three assists in 31 appearances since joining the Premier League outfit.
Brighton sit sixth in the table, just five points behind fifth-place Tottenham with a game in hand.