The Argentine midfielder has been sidelined since January 20 after suffering the knock in the 1-1 draw against Bournemouth at the London Stadium.
Lanzini has missed the Hammers' last four matches with the issue but has stepped up his training and is edging nearer to full fitness.
"I'm feeling good," the 25-year-old told the official West Ham site. "My injury is getting better every day and I'm expect to be back very soon. I'm training hard and I expect to go back with the team next week.
"It's great that Marko [Arnautovic] is back now. He is a very good player and we need him. I'm also looking forward to playing with Joao Mario. He is an important player and together we have good qualities."
Lanzini has had a hand in 11 goals during his 20 league and cup appearances for the East London outfit this term.