The Brazil international has been heavily linked with a move to Barcelona.
Liverpool have rejected a bid of €125m from Barcelona for midfielder Philippe Coutinho.
The Brazil international has been heavily linked with a move to Barcelona, who are looking for another attacker after selling former star Neymar to Paris Saint-Germain in a deal worth €222m.
According to Melissa Reddy, a third bid from Barcelona for Coutinho has been rejected by Liverpool, who earlier in the window released a statement insisting the former Inter Milan man is not for sale.
BBC Sport also believe a third bid has been made for Coutinho, who has handed in transfer request to the club he joined back in 2013 for £8.5m.
The initial bid is reportedly worth €80m up front with a further €45m in add-ons but Liverpool have immediately rejected the offer, reinforcing their claim that Coutinho is not for sale.
Coutinho was an integral part of the Reds side that finished fourth in the Premier League last season, helping Jurgen Klopp's side reach the qualifying stages of the Champions League.
Liverpool now look well set to reach the group stages after beating Hoffenheim 2-1 in the first leg but have played their first matches of this campaign without Coutinho, who is officially missing from the first-team squad with a reported back injury.
Barcelona were disappointing during the Supercopa de Espana, where they went down as 5-1 losers on aggregate to bitter rivals Real Madrid, also losing Luis Suarez to a knee injury for the opening matches of the La Liga season.
Barca played with three centre-backs in the absence of another forward on Wednesday during the second leg of the Supercopa de Espana, with Suarez playing up front with Lionel Messi.