Rodrygo has returned to field training at Valdebebas just eight days ahead of Real Madrid's crucial Champions League clash against Liverpool.
Liverpool and Real Madrid have learnt Nottingham Forest won't entertain January bids for in-form centre-back Murillo, who remains under contract until 2028.
Liverpool are reportedly planning to sign Eintracht Frankfurt's Omar Marmoush to replace Mohamed Salah, who has described his countryman as a "unique talent".
Liverpool striker Mo Salah says he wants nothing less than to win the Premier League in what is likely to be his final season with the Anfield club.
Liverpool owners FSG believes Trent Alexander-Arnold will reject Real Madrid's advances and sign a new deal at Anfield.
Liverpool and Tottenham are reportedly targeting Hugo Larsson, who could command a £70m fee, potentially making him Liverpool's third costliest signing and Spurs' record buy.