Diamanti played alongside Parker at West Ham during the 2009/10 campaign and is hoping to put one over his old colleague.
"I would really like to face and beat Parker, who was a team-mate of mine at West Ham," Diamanti said in today's press conference.
"Parker is a top player, a great rival, but since I left (West Ham), I haven't spoken to him."
Diamanti, who scored seven goals in 30 league appearances for Serie A side Bologna last season, is confident about his side's chances heading into this weekend's match but, although he feels Italy are superior to England, he is taking nothing for granted.
The Azzurri finished second in their pool behind holders Spain, while England topped Group D.
"Perhaps in terms of the things that surround football like stadiums, fans' behaviour, they (English) are 30 years ahead of us, but when it comes to the pitch, we are much stronger and play a more beautiful football," Diamanti said.
"However, even if history says that we are much stronger than them, it doesn't count for anything in these types of games.
"I have only watched England's game against Ukraine and they are strong side, with great champions.
"It's going to be a big battle, we respect them but we have no fear."
Diamanti is hoping he will get the chance to feature in the quarter-final having made his debut in a major international competition in Monday's 2-0 triumph over the Republic of Ireland.
"I was very excited to make my debut against Ireland," the 29-year-old said. "Now I have a chance to play in a game that only a couple of years ago I could only dream of playing on the PlayStation.
"I never gave up hope and I've worked hard for it.
"I will do everything that I can to help my team progress to the next round."
Even without playing, Diamanti is enjoying the adventure in Poland and Ukraine and says training alongside veteran playmaker Andrea Pirlo is a privilege.
"I'm having a lot of fun and it's great to play alongside Pirlo," he said. "The past couple of days have reconfirmed to me that Pirlo is the strongest player in the world."
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.