The Sun says Harry Redknapp's QPR have made a shock move for the Swedish international, who signed a new four-deal to remain at the Hawthorns in October.
Arsenal have also been monitoring the centre-back and Olsson, 29, wants to move to the capital as soon as possible.
A source close to Olsson said: "Jonas loves it at West Brom but there are personal reasons why he wants to go to London. It is about his family. But it has been a hard decision as West Brom have been great for him."