In a letter to the chair of the Nobel Peace Prize Committee, Thorbjørn Jagland, the group wrote: "The efforts to normalise relations between the two countries have been unprecedented and have created the opportunity of lasting peace and cooperation in the region."
The proposal comes four weeks after representatives from the US Congress submitted a similar letter, nominating the same three candidates to receive the prestigious award.
Representatives from the US Congressional Albanian Issues Caucus offered considerable praise for prime ministers Dačić and Thaçi, in their letter to the Nobel Committee last December. "In breaking sharply with the past and finding a path to a brighter future, the two Prime Ministers showed remarkable commitment, courage, and vision," they wrote.
But the nomination of the two Balkan leaders is likely to raise eyebrows.
Prime Minister Thaçi, who is the former leader of the Kosovo Liberation Army (KLA), is regarded as a war criminal in Serbia.
According to a report by Council of Europe rapporteur Dick Marty, a former Swiss prosecutor, Thaçi served as a mafia-like crime boss during the Kosovo War. Accusations against Kosovo's prime minister included leading a group that supposedly committed assassinations, beatings, harvesting of organs, drug-trafficking and other crimes.
Meanwhile, the nomination of Serbian prime minister Dačić is also expected to generate controversy.
Prime Minister Dačić served as an anti-Western spokesman for notorious Serbian and Yugoslav leader Slobodan Milošević, who died in a prison cell in The Hague on trial for genocide and other war crimes.
Today, Dačić says Serbia's future is in the EU, but many in the Western world doubt the authenticity of his apparent change of heart.
'Last push for lasting peace'
The S&D's letter to the Nobel Peace Prize committee is dated 24 January and signed by the Austrian MEP Hannes Swoboda, who is head of the group in the European Parliament.
In the letter, Swoboda writes that the nomination of Ashton, Dačić and Thaçi is not only meant "as a reward for the progress achieved already, but also as a motivation, possible as the last push that is needed for lasting peace".
"Relations between two key players, Kosovo and Serbia are fragile - but they exist", Swoboda writes. Nevertheless, the European Community was not able to prevent the Yugoslav War, a conflict which resulted in 140,000 victims, the Austrian politician continued.
"Lessons from other conflicts around the world have taught us that sometimes there is only a small window of opportunity to substantially advance peace," Swoboda writes, noting, "I believe that today we are witnessing this window of opportunity between Kosovo and Serbia."