According to the Daily Mail (h/t Daily Star's Harry Howes), the Scottish Premiership champions value the Frenchman at £30 million, but the Seagulls will test their resolve with a slightly lower offer.
The south-coast club's transfer record is just £13.5 million, which they paid for Jose Izquierdo in the summer.
They have made a fine start to life in the Premier League after last season's promotion from the Championship, but more improvements can be made.
Dembele left Fulham for Celtic in 2016 and was an instant hit in Scotland, scoring early and often. He was a standout in the league but really made headlines in Europe, most notably thanks to a starring display against Manchester City.
The 21-year-old scored twice in a spectacular 3-3 draw, including this athletic effort, per UEFA.tv:
He has scored eight goals this season but has been hampered by recurring hamstring issues following a tear suffered in last year's Scottish Cup semi-final against Rangers. When healthy and at his best, he's still looked like the talent coveted by a ton of clubs.
Chelsea have a good option of their own at the striker position in Alvaro Morata, but depth has been an issue. Michy Batshuayi has made the most of limited opportunities, but manager Antonio Conte doesn't appear to rate the Belgium international highly and has barely started him.
As shared by Sky Bet, the Blues have made some odd decisions when it comes to Batshuayi:
Chelsea need more options to compete at every level, and signing a talented prospect who could develop into a star appears the way to go. Dembele would fit that category, and he likely wouldn't mind sitting behind Morata to start his career at Stamford Bridge.
A move to Brighton could be appealing as well, though. Glenn Murray has been a fine option up front for the Seagulls, but he's 34 years old and not the fastest striker around―Dembele would fancy his chances of beating him out for a starting position.
Celtic haven't been beaten in Scotland for 67 games and can afford to cash in on one of their stars without skipping too much of a beat. Per Scouted Football, they even have options within the squad to replace him in January:
No Moussa Dembele (21) for Celtic, no problem!— Scouted Football (@ScoutedFtbl) December 2, 2017
Odsonne Edouard (19) went beast mode earlier today against Motherwell, bagging a hat trick in a 5-1 demolition of Motherwell.
He saw his opportunity to impress the gaffer, and he snatched it right up. pic.twitter.com/X50zTeKlah
A move to the south coast could be the perfect springboard to greater things for Dembele, who has already shown he isn't afraid to think outside of the box―few young players would have made the move from London to Glasgow to begin with.
If Chelsea still want to land the talented forward, they will have to make their move before Brighton have the chance to close the deal. The Seagulls struggled to bring a striker in the summer, however, and with Celtic looking for a higher fee, there appears to be plenty of time left for the Blues.