Heidfeld left the role after his third Pirelli tyre test at Jerez late last week because he is returning to the formula one grid with Sauber.
Former Renault racer and GP2 driver Grosjean, 24, will replace the Sauber-bound German when F1’s incoming official tyre supplier moves its 2011 programme to the Monza circuit this week.
But it has not been confirmed that the Swiss-born Frenchman will be staying in the role beyond his Italian outing.
“I am doing two days at Monza on Tuesday and Wednesday,” he told Auto Hebdo in a French-language interview.
“After this test the decision will be made about continuing together or not. I hope to be with the project until the end,” added Grosjean.
“I’m anxious to get behind the wheel of a formula one car again, especially as this Toyota was clearly one of the best cars at the end of last season.
“To be again accumulating kilometres in an F1 car is of course a good step towards returning to F1 soon,” he said.
Grosjean attended the Jerez test last week, before travelling to Toyota’s Cologne headquarters for a seat fitting.
“Nick told me the TF109 is very good and very neutral, which is the perfect way to test tyres,” he added.
© RIF | GMM