The FIA has banned Frenchman Grosjean for one race after causing the crash that ended championship contenders Fernando Alonso and Lewis Hamilton's Belgian Grand Prix.
Belgian d'Ambrosio, 26, is Lotus' official third driver.
The 2011 Virgin race driver is managed by Lotus team boss Eric Boullier's management arm Gravity.
"We'll announce the name of (Grosjean's) replacement a bit later in the week," said Boullier at Spa on Sunday.
D'Ambrosio, who already attends all the races, said he is ready and willing to step into the cockpit of the highly-competitive black and gold E20.
"It's unfortunate for Romain, but it's the FIA's decision. It's not for me to comment," he told the Belgian broadcaster RTBF.
"Anyway, it's part of my job since the beginning of the year to be ready, no matter what. I'm ready and highly motivated.
"What happens, we'll see. It (the situation) is still brand new and I don't know exactly what will happen."
Boullier is quoted by the French-language RMC Sport as saying the chance d'Ambrosio will get the job is "80 per cent".
"(But) there are many drivers looking for a steering wheel," he is quoted by France's autohebdo.fr. "First, we are thinking of (appointing) our third driver."