Reds officials told the Liverpool Echo that manager Jurgen Klopp has no interest in signing Gomes, who joined Barcelona from Valencia in a €55m (£49m) deal last summer.
Klopp also has no intention of pursuing a move for Gomes's teammate Rafinha, who has been linked with a £36m transfer to Anfield.
The Brazilian midfielder is seen as injury prone and not of a sufficient quality to enhance the Liverpool team, according to the Echo.
Barcelona remain interested in signing Coutinho even though they had an €80m offer for the player rejected by Liverpool in July. The Catalan club want Coutinho as a marquee signing to replace Neymar, who is expected to depart Camp Nou in a world-record £198m transfer to Paris Saint-Germain.
Coutinho signed a new five-year contract without a buyout clause at Anfield in January. He said in June that talking about speculation linking him with a move to Catalonia was "complicated".
Barcelona president Josep Bartomeu refused to rule out a fresh offer for Coutinho last week, saying that the club would bring in at least one midfielder before the transfer window shuts.
"He's a Liverpool player and I have a lot of respect for Liverpool. What we do in the summer is to be very discreet about everything, so we cannot confirm or deny anything," he was reported as saying.
"There will be more players (coming in), one in the middle, for sure."
Coutinho scored 13 goals in 31 league appearances for Liverpool last season to help the club qualify for the Champions League.
His form was rewarded with a new long-term contract worth around £150,000 per week in January, making him the highest-paid player at Anfield.
Brazil manager Tite encouraged Barcelona to make a move for Coutinho in May, saying the 25-year-old would be an ideal signing for the Catalan giants.
"I don't want to be pretentious and give an opinion on Barcelona, but who wouldn't want a player like Coutinho?" he was reported as saying by ESPN.
"That magic, that capacity to invent and create something, that change of rhythm, the way he builds play – it's crucial for any side."