The 19-year-old has emerged as Liverpool’s top target as they seek to sign at least one more midfielder this summer.
Lavia is keen to move and has already agreed personal terms on a contract with the Merseyside giants ahead of a potential transfer.
Southampton were quick to reject Liverpool’s opening bid for the player but the Reds are now about to table a second bid.
It has been claimed that Liverpool are all but ready to slap in a new bid worth £42.5m in a guaranteed fee for the midfielder.
The Reds are ready to offer another £2.5m in add-ons to take the full package to the figure of £45m.
It would still be short of Southampton’s £50m asking price for Lavia but the Reds are prepared to go close to the figure.
The Merseyside giants are also wary of interest from Chelsea in Lavia and want to do a quick deal to sign him.
It remains to be seen whether Southampton accept the new offer once they receive it from Liverpool.