De Rossi has called a media conference for Tuesday when he is expected to confirm his future plans.
Roberto Maninci is a confirmed fan of the 29-year-old Italian star, who only signed a new long-term deal with his hometown club in February.
Some reports in Italy have claimed that City are on the verge of agreeing a deal with both Roma and De Rossi.
But Zeman remains hopeful his midfield talisman will remain at the Stadio Olimpico.
"I am convinced that De Rossi stays with us," said Zeman.
"He is very important for us and the club has not asked me anything about him. I think he will remain.
"Has Mancini have ever called me? Several times, even when I was at Pescara last year. The last time I heard from him was three weeks ago. "
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
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.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
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.
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.