Celtic’s young striker has been a revelation in Scotland this season and drawn attention from Europe’s elite.
Chelsea boss Antonio Conte tried to bring Dembele to Stamford Bridge in the January transfer window but was foiled in a late swoop.
The Hoops are said to value their 20-year-old hitman at £40million, with Rodgers experienced in handling talented prodigies.
Moussa Dembele has six goals in his past two games for Celtic
When he was manager at Liverpool, Coutinho and Sterling flourished under his leadership and almost helped secure a first Premier League title.
Sterling was subsequently sold by Rodgers for £49million to Manchester City before suffering the sack at Anfield.
Philippe Coutinho, meanwhile, has committed his long-term future to Liverpool by signing a club-record contract.
And Rodgers sees as big a future ahead for Dembele.
Philippe Coutinho and Raheem Sterling were key in their youth under Brendan Rodgers at Liverpool
Stars who have played in both Scottish and English Premier Leagues
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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)
I took Coutinho from Inter Milan at 19, Sterling at 17
"He’s got huge potential," Rodgers said. "He’s just turned 20 years of age.
“I’ve worked with some really top young talents.
“I took Coutinho from Inter Milan at 19, Sterling at 17, Suso I put in the team and he’s at AC Milan now.
“He’s certainly up there with the big talents. He has a fantastic mentality which helps him.
Antonio Conte may look to bolster his Chelsea attack in the summer by going for Moussa Dembele again
“He has talent but he’s also very focused on being a footballer."
Chelsea could return with a fresh approach for Dembele in the summer transfer window.
The France Under-21 international has continued to shine since staying put at Celtic last month, having netted two hat-tricks in his past two appearances.