The Reds made a surprise move by signing Colombian striker Luis Diaz from Porto on Sunday.
And The Liverpool Echosays Jurgen Klopp wants to recruit Carvalho prior to Monday's 11pm deadline.
However, Liverpool are determined not to pay over the odds for Carvalho, who will be a free agent in the summer.
It is believed they are willing to pay £5m to sign Carvalho.
Chelsea, West Ham United and Real Madrid are just a few of the clubs who shown an interest in the 19-year-old.
England U18 international Carvalho has scored seven goals in 16 Championship appearances this season.
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