The Red Devils have been tracking the 22-year-old for some time, with former manager David Moyes having made him a rumoured top target for this coming transfer window before he was sacked a matter of weeks ago.
Since then United’s interest is understood to have cooled, which has alerted Liverpool.
After watching his Reds side concede a whopping 50 goals last term – which ultimately cost them a first ever Premier League title – Brendan Rodgers is thought to be eyeing defensive minded additions.
Carvalho – who has represented Portugal twice at international level – is thought to be an option, with the Northern Irishman having been impressed with his ability to shield his teams’ backlines.
The youngster has a £37m release clause in his contract, yet it is rumoured that offers of closer to the £30m mark will be accepted by Sporting, who are in a state of financial worry.
Liverpool may be able to fund a deal, yet much depends on their pursuit of Adam Lallana – with Southampton now demanding upwards of £25m for the playmaker.