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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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.