HITC Sport understands Cardiff eye move for Wales international forward.
New Cardiff boss Paul Trollope is on a recruitment drive of Welsh players after being told by Bluebirds owner Vincent Tan to get more young Welsh talent into the team.
Cardiff have already signed Wales defender Jazz Richards from Fulham this summer and they are now eyeing a move for his international teammate Williams in a second raid on the Cottagers.
Williams was a member of Chris Coleman's Wales squad for this summer's Euro 2016 finals, but he did not make an appearance during the tournament in France.
Williams, who made his debut for Fulham in August 2014, is highly regarded at Craven Cottage, but he finds himself down the pecking order in Slavisa Jokanovic's first-team plans.
The 20-year-old made just one appearance for Fulham last season after recovering from a serious knee injury he picked up in March 2015.
The former MK Dons youngster enjoyed a spell out on loan at Gillingham at the back end of last season and he made 10 appearances during his time at Priestfield.
Cardiff chief Trollope is a big fan of Williams having worked with him in the Wales set-up and he is hoping to bring the versatile forward to the Cardiff City Stadium to bolster his attacking options.