Olsson has a season left on his contract with Albion, where he has spent the last five years, and the club would rather cash in at a reasonable fee now than lose him on a free next summer.
Rosenberg said: "We stayed for one month in Europe together [at Euro 2012] and my manager was telling me about West Brom. I talked about everything to Jonas - the facilities, the people, the players, the city. Everything he said was positive.
"Now I have to try to talk to him so that he stays. I saw him in the national team, and he is a fantastic player."