The 19-year-old attacker has been turning heads with his performances for Fulham in the Championship this season and helping to power their promotion bid.
Carvalho has netted seven times in 18 league outings, along with providing four assists for his team-mates, and Liverpool are impressed.
The 2020 Premier League champions contacted Fulham to enquire about Carvalho’s availability.
However, the Cottagers told Liverpool that they do not want to sell the attacker.
Liverpool regularly look to add young talents to their squad and could test Fulham’s resolve with an offer before the transfer window closes this month or in the summer.
Carvalho was born in Portugal, but turns out for England at youth level.
He progressed through the youth ranks at Fulham and was handed his Cottagers debut in the EFL Cup in September 2020.
Fulham hold a five-point lead at the top of the Championship and Carvalho looks on course to play Premier League football next term.