The La Liga giants have seen bids for both players rejected in the last week but Sunday's Spanish Super Cup first leg defeat to arch-rivals Real Madrid has served as a wake-up call for the Barcelona board.
Last season's runners up were beaten 3-1 on their own ground with club president Josep Bartomeu faced with calls to resign on social media after the match. The Barcelona dressing room also aired its disappointment over the lack of transfer activity since Neymar's €222m (£198m) move to Paris Saint-Germain, with Sergio Busquets leading cries to strengthen the squad.
According to Sport, that message has been heard loud and clear. Barcelona plan to significantly step up their attempts to bring both Coutinho and Dembele to the club and want both players signed before their La Liga campaign gets underway against Real Betis on Sunday.
Coutinho, 25, handed in a transfer request on Friday just hours after Liverpool's owners Fenway Sports Group released a statement insisting that no offers will be considered following a €100m offer from the Nou Camp.
Barcelona remain undeterred however and are still confident of striking a deal. The Brazil international missed Liverpool's opening game of the Premier League season against Watford on Saturday and also did not travel for Tuesday's Champions League qualifier against Hoffenheim, with Sport suggesting neither the club nor the player want to risk an injury that would hold up a move.
While Barcelona see Coutinho as a long-term replacement for captain Andres Iniesta, Dembele would be tasked with filling the void left by Neymar.
Last week, Dortmund confirmed they had rejected an offer – also said to be worth €100m – and suspended the France international until further notice after he failed to report to training. The club have not ruled out a transfer however, with reports suggesting the Bundesliga side are seeking a fee closer to €130m.
Some at Barcelona are wary of paying such an exorbitant fee for a player who only has two seasons of senior football under his belt. But such is the pressure for the Blaugrana to make a serious statement, they are determined to push on.
Sport add the deal for Dembele is more complicated than the proposed move for Coutinho, but suggest the club want to push through both deals despite the eye-watering fees.
Barcelona have reached an agreement to sign former Tottenham Hotspur midfielder Paulinho from Chinese Super League side Guangzhou Evergrande for €40m, an unpopular signing for supporters who are eager to see marquee names arrive at their club following Neymar's departure.