The 20-year-old impressed for the Seagulls having spent the season on loan at the Amex Stadium.
Chelsea are understood to have rejected a bid from Roberto De Zerbi's side, insisting the player is not for sale at any cost.
New Blues boss Mauricio Pochettino is a big fan and is expected to include the left-sided centre-back in his side next season.
De Zerbi wants to sign the defender, who made 22 appearances this season, in a permanent deal but Chelsea are insisting he is going nowhere.
Brighton's £30m bid equals their club-record deal for Joao Pedro, who has already agreed to join them from Watford.
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Colwill has featured regularly under De Zerbi, and helped the south coast club to secure Europa League football.
He has, however, risked upsetting supporters following a social media post after Chelsea's humiliating 4-1 defeat to Manchester United on May 25.
A popular Brighton fan tweeted him during the game: "Hey mate, how's your evening going?"
To which he responded after the full-time whistle with a picture of him and teammate Billy Gilmour, who joined Brighton from Chelsea last summer, all smiles.
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Holding four fingers up with a big grin, Colwill captioned the photo: "Brilliant."
His post comes after the youngster praised Brighton for trusting him when other clubs wouldn't.
In a recent interview with The Athletic, Colwill said: "Brighton have done a lot for me. They put their trust in me when others didn't and I'm a person that loves to repay that. We'll see.
"I don't know what is going to happen (at Chelsea)."
Asked about whether another loan deal could be on the cards, he remarked: "Who knows, we'll see what happens in the summer.
"I love the Brighton fans, I love everything about them (the club). I'll take that into consideration."
The publication also had to remind the star he will still a Chelsea player.
"I forgot for a minute," he said, before waxing lyrical about his team-mates, and playing under De Zerbi.
"When Roberto came in (last September), he just changed things. His mentality as a manager is world class and he is definitely going to be one of the best managers in the world — if he's not already.
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"That's what you need at a club like this, that's what you need to take us to the next level. I never realised how good the players are and he's come in and playing the style — oh, it's amazing.
"It fits everyone in the changing room. That's why they are all playing outrageous football."