Rodgers has spent £25million already this summer on the likes of Fabio Borini and Joe Allen.
Tello has failed to become a regular at Barcelona and has long been linked with a move away from the club.
The Sun reports that Liverpool are keen on signing Tello on a season-long loan with a view to a permanent deal at the end of the season.
Tello has just 12 months left on his current contract with Barcelona.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?