Barca expect Tottenham to return with another offer before Tuesday's transfer deadline but sources have told ESPN it would have to be a "huge" offer for the club to consider selling.
Emerson, 22, re-joined Barca for €9m this summer after spending the last two years at Real Betis, who would be due a percentage of any future transfer fee.
He made his first start of the season against Getafe on Sunday. United States men's national team defender Sergino Dest had been preferred in Barca's opening two matches, with the club hopeful the competition between the two will bring out the best of both.
Coach Ronald Koeman has expressed a desire to keep Emerson but Barca's financial situation could force them to let him move to England if Tottenham were to significantly raise their bid.
Spurs, meanwhile, are in the market for a right-back and a central midfielder in the final days of the window.
Japhet Tanganga, who can also play as a central defender, has been chosen by new coach Nuno Espirito Santo to start all three Premier League games so far this season, with Matt Doherty his backup. Aurier is deemed surplus to requirements.
Ilaix's contract expires at Camp Nou next summer and he's not reached an agreement to renew. Barca will let him leave if a club pays around €20m. If not they will leave him in the stands until his contract runs down.
Leipzig's first offer was worth around €6m but sources say they could make a renewed attempt to sign Ilaix, who made 18 first-team appearances for Barca last season, if midfielder Marcel Sabitzer joins Bayern Munich in the coming days.