Poland's surprise home defeat by fellow Euro 2012 co-hosts Ukraine on Friday has given the top two a substantial advantage ahead of this week's encounter in Podgorica.
It offers Roy Hodgson's men something of a safety net should they be unable to secure the victory they crave.
However, Cleverley is adamant that is not the attitude England intend to take into the game, knowing three points would take them so much closer to their overall aim.
"Yes, a draw would be a decent result," he said.
"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.
"It is a significant game but we are going out to win it. Two wins from these two matches would be really satisfying."
Cleverley accepts the contrast from Friday's eight-goal mauling of San Marino could hardly be greater.
Whereas San Marino barely had an attack of note, Montenegro will be cheered on by a partisan crowd, creating a frenzied atmosphere England found very difficult to cope with on their only previous visit 18 months ago.
Yet Cleverley does not view that as a particular problem.
"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 most obvious example of someone getting wrapped up in the atmosphere was Wayne Rooney, famously sent off for kicking out at Miodrag Dzudovic.
It earned the Manchester United man a two-match suspension and ensured he was not fully battle-hardened when he entered the Euro 2012 fray last summer.
Those kinds of experiences are ones which Cleverley has so far managed to avoid as he tip-toes through the early days of his international career.
Still only 23, Cleverley made his international debut in August after a successful stint with the Great Britain Olympic team.
Yet so rapid has his rise been that the midfielder 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."
Changes are anticipated though.
Skipper Steven Gerrard is certain to return in midfield, where there is a chance he will be joined by Michael Carrick, whose ability to retain possession is a priceless asset in such a frenzied atmosphere.
Chelsea's Ashley Cole is set to return at left-back, with Glen Johnson set to overcome a toe problem on the right.
And Danny Welbeck also seems sure to have some involvement, having proved in the recent Champions League clashes with Real Madrid what an effective performer he can be on the biggest stage.