Clarke wants the Baggies to add competition in that position for current number one choice Liam Ridgewell after Nicky Shorey's summer departure to Reading.
The chances of Costa Rica international Oviedo leaving Copenhagen appear to have increased after the Danish club failed to qualify for the group stages of the Champions League.
But Albion could face a battle for his signature with Saturday's opponents Everton, who have also been linked with a move for the 22-year-old.
Olsson may prove more difficult to prise away from Ewood Park as he still has nearly two years remaining of his current contract and so is likely to command a sizeable fee.
Clarke, who has made five signings so far this summer, is also understood to have made an inquiry about Rubin Kazan defender Cristian Ansaldi.
But Oviedo and Olsson are believed to be his first-choice priorities if a deal can be struck for either in the next 36 hours.
Meanwhile strikers Peter Odemwingie (thigh) and on-loan Chelsea player Romelu Lukaku, who has suffered an unspecified knock, are expected to be fit to face the Toffees.