Suso has been strongly linked with Milan, whilst one report this week linked Raheem Sterling with Real Madrid.
Liverpool midfielder Suso's representatives are meeting with the club's representatives over the Spaniard possibly signing a new deal at the club, according to manager Brendan Rodgers.
Rodgers mentioned a new contract for the 21-year-old during his press conference previewing Saturday's Merseyside derby against Everton at Anfield.
Suso, who scored in the penalty shootout win over Middlesbrough in the League Cup this week, has been strongly linked with a move to Serie A giants Milan.
The Liverpool boss was also asked about the contract situation surrounding Raheem Sterling, who has been linked with a move to Real Madrid according to one report in the press.
Rodgers said: "We think it shows he's obviously playing exceptionally well but I think you can link Raheem with every club in the world at the moment.
"I sit easy with it. Sterling's still got three years left on his contract, so there's no rush from my side."
The news will be welcome amongst many Liverpool fans ahead of this weekend's game. Some have often questioned the logic of letting a promising player like Suso go whilst reports linking him with Milan have been circulating. From pre-season and in his cameo against Middlesbrough, it shows how much good that a year on loan at Almeria has done for him. He looks stronger and wiser on the ball.
As for Sterling, it's a welcome stance that Rodgers has taken. There's no sense of panic from the club because they see no reason to, and the 19-year-old will be offered a deal in good time but not right now.