According to Mail Sport, the Reds could return with a second bid for the Sweden international only if the Magpies first make progress in signing a replacement.
The reigning Premier League champions are unwilling to submit another offer while Newcastle remain in limbo, awaiting responses from their striker targets.
Top of their list is Benjamin Sesko, for whom a £70 million ($92m) bid has reportedly been made, while other options include Yoane Wissa and Ollie Watkins.
"I know where he is, really, through the media. From that perspective, it's difficult for me to go into any kind of detail. The situation is far from ideal and is quite complex,” manager Eddie Howe had said
"I was made aware of a bid yesterday (Friday) and that bid was turned down, all before I'd even heard about it. People back in England are dealing with the situation.
“I don't know what happens next. From our perspective, we still support Alex in every way and my wish is that we see him in a Newcastle shirt again.”