The Atalanta playmaker was originally considered as a standby for Francesco Totti in the link role between midfield and attack.
But with Trapattoni edging towards an orthodox 4-4-2 line-up Doni could be handed a start on the left.
"Playing on the left is fine for me, it is a role that belongs to me," said Doni.
"Trapattoni has indicated that I was here to be the deputy to Totti but you could say that is not a complete picture of me.
"That is not because I am not prepared to be placed behind Totti, who is a genuine phenomenon, but because I can also cover positions that he doesn't operate in - on the left, on the right or in the centre of midfield," Doni added.
I am a midfielder and Totti is a forward. We also have different physical characteristics
Doni, 29, admitted he was unable to match Totti for attacking flair, but said he offered qualities that Trapattoni might find useful.
"Totti is clearly better than me in forward play and he can also play as a support striker, part of a front two," he said.
"To sum up the situation in a few words, I am a midfielder and he is a forward. We also have different physical characteristics."
Doni is a late developer who, after starting his career in the fourth division with Rimini, was still playing Serie B football with Atalanta two years ago.
Doni has suffered some slight muscle problems during Italy's preparations but thinks he will be fully fit for the Ecuador game.
"I have got over the little knocks and am much better, it is just a question of reaching the maximum physically. I think I will be ready for Monday - if needed," he said.