Diaby, whose red card in the 4-4 draw with Newcastle on Saturday when his team were 4-0 up was arguably the pivotal point in the match, offers a similar presence in the centre of the field to Vieira, formerly of Arsenal but now with Manchester City.
Vieira was part of the France squad which won the 1998 World Cup and Euro 2000 titles, and has tipped Diaby to be his successor at club and national team level. The 24-year-old is flattered by Vieira's comments and is determined to put his injury problems behind him to follow in Vieira's footsteps.
"(Vieira's comments) are an honour for me, but it will require some work to reach his level and achieve what he did," Diaby told L'Equipe. "I hope to get there one day, and perhaps even achieve more.
"Above all I admired his performance in the France team. He won everything. For now, I have gained nothing. So, if I can start winning some trophies, it would not hurt."
Asked if he could play a leadership role for Les Bleus, Diaby added: "Yes, of course. Why not? At one point, I think we should be ready to take the lead. If I was asked to do that, I would assume my responsibilities."
Injuries have badly affected Diaby's season so far. The Paris-born player was troubled by an ankle injury for much of the first half of the season and then injured his calf in December before making his return to action in the FA Cup fourth-round clash with Huddersfield last month.
"It's very annoying. It's hard to watch my team-mates practise on a daily basis while you're on the massage table and you see them. It's difficult," he said, "but in these moments, the most important thing for me is to look after myself so that I come back in perfect shape."
Diaby, who is part of the France squad for the friendly against Brazil on Wednesday, must now serve a three-match domestic ban following his dismissal at St James' Park.