Pereira has been the subject of interest from a number of clubs during the summer with Marseille, Juventus and Chelsea among the teams to have monitored the Brazil midfielder's situation.
And it is understood Forest are the latest team to have emerged as a potential suitor for the 28-year-old ahead of Friday's deadline.
Pereira has been a key player for Fulham since his arrival from Manchester United in 2022.
The attacker has started both of Marco Silva's side's Premier League games this season and having lost Joao Palhinha to Bayern Munich earlier in the summer, the Craven Cottage side will fight to keep Pereira, who has two years on his existing deal with the west London club.
Nottingham Forest are interested in signing Fulham's Andres Pereira before the window shuts
Meanwhile, Forest's move for Eddie Nketiah has collapsed with sources insisting the deal is very unlikely to be revived.
Arsenal striker Nketiah was on the verge of joining the City Ground club last week, with a medical booked.
But the transfer has broken down with indications being that the deal won't be revisited.
Crystal Palace have a long-term interest in Nketiah and considering launching a formal offer for the forward.