No Premier League players made the top 10. Leicester and Algeria winger Riyad Mahrez and Foxes and England striker Jamie Vardy finished 11th and 12th respectively, while West Ham and France midfielder Dimitri Payet came 13th in the vote.
The list will be cut to three players in August, with a Uefa panel deciding the winner during the Champions League group stage draw in Monaco on 25 August.
Barcelona’s Ballon d’Or winner Messi will be hoping to pick up his third award after claiming the inaugural prize in 2011.
Schmeichel, 29, told BBC East Midlands Today: “I can assure you the hunger is 100% still there.
“We have to go again, do exactly the same again and see where it takes us.”
Schmeichel was an ever-present for the Foxes in the Premier League last season.
The Dane was speaking prior to France midfielder N’Golo Kante’s move from the King Power Stadium to Chelsea for a fee believed to be in the region of £30m.
The club begin the new campaign against Manchester United in the Community Shield on Sunday, 7 August, with their Premier League title defence beginning six days later when they visit promoted Hull City .
‘We trust each other’
Former Manchester City, Notts County and Leeds United goalkeeper Schmeichel said no specific goals had been set for the new season.
“We have never said ‘this is what we are aiming for’,” the Dane said. “We go out, we work hard for each other and do our best. That is all we ask of each other.
“If someone is not pulling their weight – which barely ever happens – then they will be told. Part of being a really good squad is the togetherness and being able to trust each other.
“We know that each day we go out on the training pitch or play a game that everyone is on it and everyone will give everything they have got.”
BBC East Midlands Today’s Tom Brown
“I felt like I’d asked the wrong question. Kasper Schmeichel just looked at me, staring me down as he might a striker before a penalty, before slowly delivering the one-sentence answer I deserved when I enquired about their motivation for the season ahead.
“‘I can assure you the hunger is 100% still there’,” he said.
“So there we go. Leicester City are not satisfied by just winning the Premier League once. In fact, the club that’s grown used to defying expectations is ready to do it all over again.
“According to most bookmakers, the Foxes are more likely to be relegated than retain their Premier League title next season.
“The departure of N’Golo Kante has fuelled opinions that Leicester will struggle this time out. But Schmeichel’s steely determination was clear to see – as he also pointed out they’re not going into the Champions League to make up the numbers.
“Just like his manager, he’s aiming for even more success.”