The Frenchman has had a horror 2018 season so far, including his crash behind the safety car at Baku and a penalty for causing the Barcelona start pileup.
Until now, Haas team boss Gunther Steiner has defended Grosjean.
“I’m a bit surprised how calm the team is about it,” former F1 driver Karl Wendlinger told Servus TV.
“I can imagine Gene Haas exchanging a few serious words with him in Monaco.”
At the same time, two drivers in particular are pushing hard to find a race seat.
Ferrari is championing the efforts of its junior Antonio Giovinazzi, while Pascal Wehrlein is also linked with Toro Rosso, where he could replace Brendon Hartley.
When asked about the prospect of replacing Hartley with Wehrlein, Red Bull’s Dr Helmut Marko told Auto Motor und Sport: “That’s not the intention at the moment.”