While Poland's surprise home defeat to Ukraine on Friday has given the top two in Group H an advantage ahead of Tuesday's encounter, Cleverley is adamant England will be going all out for the win.
"We are first and second in the group at the minute. And with Ukraine beating Poland, there is a bit of distance between ourselves, Montenegro and the rest," he said.
"It is a significant game but we are going out to win it. Two wins from these two matches would be really satisfying."
The Manchester United midfielder is aware the game will be a great contrast to Friday's 8-0 thrashing of San Marino, but remains unfazed at the stark improvement in opposition.
"I don't think the adjustment from one type of opposition to the other will be that difficult," he said.
"We know the job we have to do. As long as we all work hard and play our football in the right way, we can get the job done."
The 23-year-old made his international debut in August after a successful stint with the Great Britain Olympic team, and he is the only man to start every England game this season.
"I have only had a short international career but I have played in some big games, against Brazil and Italy and the World Cup qualifiers," he said.
"I have had some good experiences in my short time with England. Hopefully Tuesday will be another."