Coutinho is said to be wanted by Barcelona as the Catalan side prepare for life after Neymar, who is heading to Paris Saint-Germain in a world record deal.
It is claimed West Ham have already held talks to renew Lanzini's £30,000-a-week deal, with wages of £50,000-a-week reportedly on offer.
But unlike Michail Antonio and Pedro Obiang, the Argentine is yet to commit his future to Slaven Bilic's side.
According to The Sun, the Hammers may have to stretch to £85,000-a-week if they want to keep Lanzini out of Liverpool's clutches, having broken the £100,000-barrier for new recruits Marko Arnautovic and Javier Hernandez.
Lanzini signed for West Ham on a permanent basis in early 2016 and has three years left on his existing contract.
West Ham United midfielder Manuel Lanzini
Nevertheless, a move to Liverpool could potentially maximise his earnings.
How much should West Ham pay Lanzini as they seek to ward off Liverpool?