The 21-year-old, has been in fine form so far this season, notching six assists and two goals in eight league appearances.
And it is thought that the Reds’ boss, who missed out on several summer transfer targets has been monitoring the youngster as a possible solution to his lack of central midfield options.
Atletico, however, currently second behind Barcelona in La Liga, are unlikely to let their protégé leave on the cheap and speculation suggests that a bid of around £17m will be required for his services.
But Liverpool, who themselves have issued a statement of intent this term after just one defeat in their opening seven fixtures could reward Rodgers’ impressive turnaround of the club by sealing a deal for the Spain international, who many deem instrumental to Diego Simeone’s side’s unbeaten start to the campaign.
Should any bid be accepted, though, the Anfield club will need to offer the player a persuasive package, after his rapid development under his current boss saw him sign a new contract until 2018 in recent months.