The tiny Adriatic republic, with a population of just over 620,000, enjoyed 1-0 wins at home to Wales and away against Bulgaria and Savicevic believes Friday's home game versus Switzerland is crucial for their bid to reach the finals.
"It's early days yet but a win against the Swiss would put us in a really good position to finish runners-up in Group G and clinch a playoff berth," he told Reuters on Wednesday.
"The most important thing is to avoid dropping points against other teams vying for a second-place finish because England are almost assured of winning the group.
"Anything we come away with against England, home or away, would be a real bonus but we shouldn't have unrealistic hopes of finishing ahead of them," said Savicevic, who scored 19 goals in 56 appearances for the former Yugoslavia.
Should the Montenegrins avoid defeat against the Swiss they will top the group ahead of England, who lead on goal difference, ahead of their clash at Wembley on Tuesday.
Montenegro will be missing prolific Fiorentina striker Stevan Jovetic and Spartak Moscow midfielder Nikola Drincic through injury, leaving Roma's Mirko Vucinic to spearhead the attack in a probable 4-3-2-1 formation for the two matches.
LEARNING EXPERIENCE
Montenegro played in the 2006 World Cup as part of a state union with Serbia before the last two remnants of the former Yugoslavia parted company.
The Montenegrins had a rough ride in their first adventure as an independent nation, the 2010 World Cup qualifiers in which they won only one of 10 matches and finished second-bottom of their group ahead of Georgia.
Savicevic, who won the European Cup with Red Star Belgrade in 1991 before capturing three Serie A titles and the 1994 Champions League with AC Milan, saw Montenegro improve quickly after taking over as the FA chief in 2004.
"We played well in the 2010 World Cup qualifiers but lack of experience and bad luck in some of the matches cost us a lot of points and we didn't do as well as we should have," he said.
"It was a learning experience and I think we have matured as a team, although the away win against Bulgaria in Euro 2012 qualifying came as a real surprise after we beat Wales in the opening match.
"I think the other teams in our qualifying group are now taking us seriously, the Swiss have come to our capital Podgorica two days before the match to prepare and it shows they have a lot of respect for us," he said.
