The Hammers are not opposed to parting with the Argentine attacking midfielder.
But the 27-year-old, who arrived for roughly £9 million in 2016, would have to go for a significant fee.
And football.london says with the source claiming West Ham want to secure a roughly £6 million profit on the player.
Manager David Moyes is revamping his squad and may see Lanzini as surplus to requirements.
The player had a poor season, with two assists and zero goals, and the club want to establish a core of up and coming British talent.
Selling Lanzini would free up funds for Moyes to spend on players of his choosing.