Chalobah, on-loan at Watford, is set to face Austria this week.
"We've got characters," he said. "Everyone wants to be successful and be able to say they have won the Under 21 championship.
"I think at the moment we're just taking it as it comes, taking it game by game and until the squad comes out we will keep our head down.
"We've got quite a bit of a record at the moment. We've got a lot of characters in the changing room and want to keep maintaining our standards and keep doing well.
"It would be a big, big achievement to go to the tournament. Playing for the Under 21s is a big achievement on its own but I think going away to Israel would show how well my season has been going."