Grosjean has been handed a one-race ban for causing a major startline crash in Belgium - which means he will miss next week's event at Monza.
And although Lotus says that it is going to wait a bit more before committing to its decision, team principal Eric Boullier admits that it is likely that d'Ambrosio will be called up.
When asked about the chances of the former Virgin racer being given his opportunity, Boullier said: "Very high.
"There are many drivers around who are looking for a drive. We will consider first Jerome, who is our third driver. He has most of the chance to drive the car.
"But I need to sit down with him. I need to do a couple of things and then we will see."
D'Ambrosio raced for Virgin in 2011, but was replaced by Charles Pic for the start of this season.
He has already driven this year's Lotus E20 at the Mugello test, which took place after the Bahrain GP.