Defence Minister Karin Enström told the Svenska Dagbladet newspaper that the decision could be approved on Thursday. The move follows months of speculation after the Swedish military asked the government to discuss the matter with Nato last autumn.
Talks are believed to now be complete with both Sweden and Nordic neighbours Finland set to sign up to the deal.
Under the 'host country agreement' Nato would be able to carry out military training in Sweden. The agreement would also include a guarantee for the safe transportation of troops by land, air or sea.
"We have come very far and it may be a government decision on Thursday," Enström told the newspaper.
Enström said Nato would not be able to deploy in Sweden against the government's wishes.
The decision is unlikely to be a precursor to Sweden becoming a fully fledged member of the alliance, according to the National Defence College (Försvarshögskolan).
Sweden has participated in Nato operations since the Bosnian war in the early nineties. In March The Local reported that over a thousand Swedish troops participated in a Nato training exercise close to the Russian border.
In a recent survey one in three Swedes supported the prospect of the country joining Nato. Sweden is currently a Nato partner, not a member, with full membership long a bone of contention between the major political parties.