The Spaniard had appeared set to join RB Salzburg on loan but could now head to Barcelona instead.
Salzburg are managed by former Liverpool assistant boss Pep Lijnders, who rates the player highly.
Barcelona boss Hansi Flick is eager to add to his midfield options before the closure of the transfer window.
The player is in need of game time, which could lead to him departing Anfield on a temporary basis.
Bajcetic, who has made 22 senior appearances for Liverpool, struggled with injury last season.
He made his debut for Spain Under-21s last year.
RB Salzburg, managed by ex-Liverpool assistant Pep Lijnders, had been set to sign Bajcetic on loan
The prospect has been at Liverpool since 2020, when he joined from Celta Vigo's academy.
Salzburg have already signed Bobby Clark from Liverpool but they may miss out on a deal for Bajcetic.
Meanwhile, Bayer Leverkusen want Tyler Morton on loan though Liverpool would have preferred a sale and value him at around £20m.
Ben Doak could leave Liverpool on a permanent basis, with Leicester and Southampton interested in signing him.