The 27-year-old has failed to live up to expectations since arriving at Goodison Park from Lokomotiv Moscow in a deal worth £13.5million back in January 2016, and will be allowed to leave if a suitable bid comes in.
Niasse was shipped out on loan to Hull City in the second half of last season, but despite chipping in with four goals, he failed to help keep the Tigers in the Premier League.
However he did show glimpses of his ability during his time at the KCOM Stadium, and reports claim that Seagulls boss Chris Hughton is keen to do a deal.
Brighton have just broken their transfer record to sign midfielder Davy Propper from PSV Eindhoven, but chairman Tony Bloom has revealed they are willing to break it again to sign a new striker.
Everton will be looking to claw as much of their outlay back as possible, and it looks as though Brighton would have to set a new record to get Niasse on board, unless Houghton is thinking more along the lines of a season-long loan deal.