The Daily Mirror reports that Liverpool have joined Manchester United in the race to sign the 17-year-old striker.
Liverpool boss Brendan Rodgers had a three-man team to watch the youngster score twice for Fulham’s Under-21 team last week.
Dembele joined the Cottagers from French side Paris St-Germain in the summer.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.