The 30-year-old defender only signed a new two-year deal with the Baggies last October but was left disgruntled with the way they finished the season after such a strong start to the campaign.
The Sweden international believes a small squad cost them in the end and is keen for Albion to show some ambition in the transfer market this summer in the hope they can avoid a similar season next time around.
Should West Brom fail to invest in the squad then Olsson could be tempted by a move elsewhere, with Tottenham thought to be monitoring the situation.
Spurs were linked with a move for Olsson last season but the departure of Harry Redknapp from White Hart Lane saw the speculation come to nothing.
However, current boss Andre Villas-Boas could return to the Hawthorns for Olsson after confirming the release of veteran defender William Gallas on Friday.