Portuguese newspaper A Bola claims Rodgers is planning to strengthen his central midfield in January, and has targeted the Benfica star as one of his transfer priorities.
The ex-Chelsea youngster left Stamford Bridge in 2011 as part of the deal that brought David Luiz to the club, but the Blues were thought to be weighing up a move of their own to bring Matic back earlier this summer.
Liverpool currently sit joint-top of the Premier League table on 16 points, but Rodgers wants to capitalise on the strong start by strengthening at the first opportunity in the January window.
Matic, 25, has impressed in Portugal since joining Benfica and the report claims an offer in the region of £30m could be enough.
That's despite a recent declaration from Benfica chairman Luís Filipe Vieira on the club's TV channel that he will not consider bids less than Matic's €50m release clause.
Chelsea boss Jose Mourinho has been strongly linked with Matic, a ball playing defensive midfielder.
But the Blues may now face competition from an emboldened Liverpool side looking to secure a return to the Champions League for next season.
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