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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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.