Suso to join Milan when his Liverpool contract expires in the summer Getty

Liverpool midfielder Suso says he is "very happy" to be signing for Milan after completing his medical with the Serie A giants.

Suso, 21, is out of contract at Anfield at the end of the season but the Spaniard has already agreed terms and signed a four-year contract with the Rossoneri.

Reports had previously suggested Milan were keen to sign the player during the January transfer window.

While the club would appear to be happy to wait until the summer before adding him to their squad, Suso has indicated a deal could still yet be negotiated that could see him leave Merseyside before the end of the month.

After completing his medical over the weekend, Suso told Sky Italia: "I haven't spoken to [Filippo] Inzaghi yet. I came for the medical and hope it all went well.

"Do I have a message for the Milan fans? I am not here for long, then we'll see when I am able to play."

Suso has been with Liverpool for the last four-and-a-half years after being brought to the club by Rafael Benitez. The playmaker looked to have a bright future at the club under current manager Brendan Rodgers after he was handed a first-team role during the first half of the 2012/13 season, but he failed to keep his place as the season progressed.

After a season on loan back in Spain with Almeria last season, the Spain Under-21 international has struggled with injury this term and has made just one appearance for the club.

Suso's agent Jaume Serra recently confirmed to IBTimes UK that they are looking into the possibility of sealing the move to Milan this month, although the decision will ultimately come down to Liverpool.

"Liverpool already know that Suso will not play at Anfield next season but we are considering him to leave now," Serra said. "It is not easy though. We will see if Liverpool accept."