Albion are holding further talks with the Sweden international who is entering the final year of his current deal.
Sources close to the Baggies claim negotiations are "progressing nicely" with the 29-year-old who has been a key figure in the club establishing themselves in the Premier League.
West Brom boss Steve Clarke is reluctant to make any bold claims publicly on Olsson's future.
But he did say: "Jonas has a year left on his contract and he understands that.
"I think he'll make decisions based on what's best for him and his family. Hopefully it's a positive decision for us."
Albion have not ruled out keeping Olsson for the final year of his present contract if talks break down.
Meanwhile, Sweden striker Markus Rosenberg has joined up with the Baggies after signing a three-year contract.
Clarke said: "He's a top international player with a fantastic goal record.
"We are an established Premier League club and should be able to attract players like that.
"His energy levels aren't yet fantastic because he's a bit behind in that respect. He will take time to catch-up with the rest but we have a good bunch of strikers."