Ludvig Åberg has already been formally selected for the Olympics in Paris and the second Swedish men's spot is likely to soon go to Alex Norén.
The qualification period ended after the US Open and on the new world ranking presented on Monday, Norén is 55th, the second-best Swede after Åberg.
Åberg is simultaneously climbing from sixth to fourth place on the ranking, a new high for the 24-year-old who will come to Olympic golf as one of the big medal favourites.
The women's qualification period ends after the PGA Championship being played this week. There, Maja Stark and Linn Grant have a grip on the two blue and yellow Olympic spots, but Madelene Sagström and Anna Nordqvist can threaten if they achieve a top placing in the major.