Piazon, 22, arrived at Craven Cottage on transfer deadline day on a six-month deal, and has since cemented himself as a regular under manager Slavisa Jokanovic.
He's been productive in helping manoeuvre Fulham into play-off contention, scoring four goals in 17 appearances in all competitions.
Fulham ran out comfortable 2-0 winners over Barnsley on Saturday, courtesy of goals from Chris Martin and Scott Malone.
Loan spell ending tomorrow but Monday I should be signing the extension!
Shortly after the victory, Piazon tweeted: "Loan spell ending tomorrow but Monday I should be signing the extension!"
Piazon, who has only made three senior appearances for Chelsea, has spent most of his career out on loan.
And he admitted his frustration at being passed around on temporary moves when he first joined Fulham.
He said: "I hope I can do a good job at Fulham. It's a good club and a traditional club.
"They have started the season well. Then I have to stay for more than one year at a club who can see me as their player and not a player from Chelsea who will one day go back to Chelsea.
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"I'm tired of moving abroad. One, two, three loans, maybe that's enough. It's time for me to stay somewhere more than one year. When they know you'll stay whatever happens, people look at you with different eyes.
"If I had the chance to go for more than one season I'd do it."