Dembele has established himself as one of Europe's rising stars since arriving from Fulham last summer.
The 20-year-old has bagged a stunning 32 goals from 46 games to help Brendan Rodgers' team sit 25 points clear at the top of the Scottish Premiership.
His fine form saw him heavily backed to move to Chelsea in January.
The Blues made an attempt to sign him only for the striker to end up staying at Celtic Park.
Stars who have played in both Scottish and English Premier Leagues
Fri, April 15, 2016
Express Sport takes a look at some of the greatest players who have appeared in both the English and Scottish top flights in recent times
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Express Sport takes a look at some of the greatest players who have played in both the Premier League and the Scottish Premier League (now Scottish Premiership)
Moussa Dembele has reportedly snubbed a move to Chelsea
Moussa Dembele would struggle to oust Diego Costa from the Chelsea XI
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However, Scottish website Glasgow Live claim Chelsea have renewed their interest in Dembele.
Club delegates requested a meeting with the forward's representatives to discuss a summer move.
They proposed a contract worth £65,000-a-week which would rise to £100,000 in due course.
But Dembele, after much consideration, turned down the offer because he wants regular first-team football.
Moussa Dembele has scored 32 goals for Celtic this season
With Diego Costa the star at Chelsea, Dembele believes his chances of regularly featuring in Antonio Conte's XI are slim.
His snub could now pave the way for a move to Liverpool.
The Reds, as well as Manchester United, are determined to snap him up at the end of the season.
But Liverpool could offer him regular football, something United cannot, and a move to Anfield might materialise.