The report claims Liverpool have made the strongest approach for the Benfica midfielder as they look to sound out his club's willingness to sell.
The Liga Sagres leaders reportedly turned down a €12m bid earlier this transfer window and are looking for at least €15m for the talented playmaker.
A number of clubs other than Liverpool and Manchester City are also interested in Gomes, including Valencia and Monaco.
A report in the same newspaper earlier this week claimed Gomes is aware of negotiations regarding his future and is open to leaving Benfica.
Benfica president Luis Filipe Vieira is reportedly willing to let Gomes go for €15m, with Gomes's agent Jorge Mendes now working through his player's options.
The 20-year-old midfielder has been called up to the Portugal national team squad in the past although he is yet to make an appearance for his country.
And he's made just two substitute appearances in the league for Benfica this season.
Liverpool boss Brendan Rodgers is still thought to be working hard to bring in reinforcements before Friday's deadline.
Reports in the English media today claim the Anfield club are ready to make an offer for Ukrainian winger Yevhen Konoplyanka.