The Gresini Ducati rider currently finds himself without a place on the 2024 grid when the team confirmed in October that it had signed Marc Marquez, after he elected to quit Honda at the end of the year.
Just as this happened, Di Giannantonio burst into the best form of his two seasons in MotoGP, scoring a maiden podium in Australia before winning the Qatar Grand Prix last week.
After that Qatar race, Ducati sporting director Paolo Ciabatti told motogp.com it was "unacceptable" that Di Giannantonio could be left without a ride for next season.
However, with Luca Marini set to join Honda next year as Marquez's replacement, Di Giannantonio looks set to take the Italian's place at VR46 Ducati.
Commenting on the situation on Thursday at the season-ending Valencia GP, Di Giannantonio said: "Yeah, I was super proud about the words of Paolo.
"He has been so good with me. Let's say that I came here with an helmet and a suit to try to test on Tuesday.
"We are working on something cool and we have good chances to test on Tuesday, and we have also now some a little more chance to be on the grid next year."
He added: "Yeah, let's say that since that bike is the only bike available – once Luca decides to make the announcement (he said jokingly) – for sure it's a great team.
"I never hid that their work behind the scenes is amazing, all the work they do together, all the guys, all the staff they have.
"They have always been super good. They joined MotoGP from Moto3, to Moto2 and then step to MotoGP.
"And they've always been super good in every class. So, that means it's a really good team. It would be a really good experience, a good challenge for me and a really good opportunity to learn things."
Marini had nothing new to offer on his future plans, stating: "I think news will come soon. So, there is not many things I can say at the moment. So, we will see in the next few days."
