Liverpool have had an opening bid of £44m for Roma goalkeeper Alisson rejected, according to Italian publication Il Tempo - via the Mirror.
Jurgen Klopp is reportedly searching for a new goalkeeper as Simon Mignolet and Loris Karius continue to prove unconvincing.
Alisson, who has caught the eye with a string of impressive performances this season, has emerged as Liverpool's prime target.
But Roma are determined to keep the Brazilian international until at least the end of the season and were not prepared to accept the Reds' first offer.
It is expected that Liverpool will renew their interest in Alisson during the summer, although with four days of the January window remaining there is a possibility of another bid.
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The 25-year-old has himself suggested, however, that any deal is likely to happen in the summer.
"It's always a pleasure to know that [big] clubs are keeping an eye on you," he told Sky Sport earlier this month - quoted by Football Italia. "Maybe we talk about it in June."
He added: “I am happy in Rome. My head is focussed on Roma. I leave my future in the hands of God.
"For now I am concentrated on Roma. Together with my teammates, we have done a great job to not allow the loss of Szczesny to be felt by the fans.
“I have worked very hard and want to continue along that track.”