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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.