The 18-year-old joined the Merseyside club from Segunda Division B side Cadiz two years ago and made his senior debut for the club against Young Boys last week.
The Spaniard also came on against Manchester United, setting up Steven Gerrard for his goal and was heavily involved in the 2-1 win over West Brom in midweek.
"The contract is something we're looking at," Rodgers said.
"Suso makes things happen. He is tactically very good and strong technically with the ball. I love that type of player.
"You saw that when he came on against West Brom for the goal. He took the ball out of a tight space. Talent finds space and he is a real talent."
Suso has represented Spain at various levels from Under-17s to Under-19s.