The Saints previously placed a £15M bid for the Portuguese winger but Liverpool rejected the offer just days before he went on to score in the clubs 3-0 victory over Manchester United.
According to CaughtOffside Liverpool have now placed a £25M price tag on the youngster and Southampton are set to return with a new bid that could match the asking price.
Carvalho has been an impressive asset for Liverpool for some time now and spent last season at Hull City where he scored 9 goals and bagged 2 assists in just 20 appearences.
Southampton have already welcomed 12 players this summer and are clearly eager to welcome more Premier League talent to bolster a side that will be looking to stay up next season.
Liverpool is said to be “open” to selling Carvalho but after recent performances many fans believe he has a place in the side especially since the club are lacking a backup winger for Mohamed Salah and Luis Diaz.
New Liverpool boss Arne Slot has been impressed with the wingers performances in preseason and could keep him if the right bid does not come in soon.