The deadline falls at 11pm tomorrow (Thursday February 1), but Fulham were dealt a blow on Tuesday night as first-choice centre-forward Raul Jimenez was forced off injured at half-time of their 0-0 home draw with Everton.
Marco Silva's side are waiting to discover the extent of the Mexican's issue, which appeared to be a hamstring strain, but they could still make a big move for Broja regardless.
According to the Evening Standard, Chelsea are keen to get the 22-year-old Albania international off their books as they look to raise cash in order to ensure they comply with Financial Fair Play (FFP) rules.
And the report adds that the Blues could be talked down from their initial asking price of £50m for the Slough-born attacker.
Broja came through Chelsea's youth system and has made 38 first-team appearances, having previously impressed during loan spells at Southampton and Vitesse Arnhem. He has scored four goals in 17 senior caps for Albania.
There could be something of a mini clearout at Stamford Bridge between now and the transfer window slamming shut, with Conor Gallagher also touted for a departure to another London club: Tottenham.
Chelsea spent lavishly during the first three transfer windows following Todd Boehly's takeover, but they have reined it in this month as they look to avoid falling foul of FFP.
The sole winter arrival in West London has been 18-year-old Jamaica forward Dujan Richards.
More Chelsea stories
Karim Benzema has been linked with a sensational move away from Saudi Arabia, and Chelsea and Arsenal are both said to be interested in the 2022 Ballon d'Or winner.
And the Frenchman is not the only striker rumoured to be on the Blues' radar as deadline day approaches...
The two-time European champions could miss out on a top Premier League target, however.
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