Cardiff will allow long-serving Kevin McNaughton to leave this summer along with Danny Gabbidon and Nicky Maynard.
Highly-rated Atletico Madrid midfielder Saul Niguez has signed a new five-year contract.
The highly-rated centre-half is yet to agree terms on a new deal at The Hawthorns and will become a free agent next summer if no contract extension is put in place.
Goalkeeper Foster considers Olsson to be a key figure for West Brom heading forward and is desperate to see the Sweden international commit his long-term future to the club - fending off mounting interest in his services.
He said: "The chairman needs to lock him in a room and hopefully get something sorted out.
"If you take everything into account I'd much rather be playing with him and Gareth McAuley than the majority of defensive pairings.
"It's people like Jonas we need to be keeping. He is such an important part of our team."