James Maddison was the subject of a second offer.
Brendan Rodgers said the England international was not for sale after the first offer was rejected.
It is thought that the second bid is worth up to £50 million.
Eddie Howe wants to add more attackers after missing out on Hugo Ekitike, who joined Paris St-Germain.
Maddison has two years left on his contract with the club.
It's not known if the ex-Coventry player would be in favor of moving to St James' Park.
Chris Wood is the only player signed by the new owners of the club.
The club's first summer window since last October's Saudi Arabian-backed takeover has seen the addition of three new players.
The club are hoping to bring in one or two more attackers before the end of the month, and they're considering the possibility of sending a player to another club.
The wages of the Germany international are likely to be a stumbling block, but they are also trying to get rid of some of their surplus players.
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