Olsen is currently on the books at Villa Park having made an initial loan move to Aston Villa permanent last summer.
The Swede is currently second choice goalkeeper under Unai Emery and has made a total of six outings in all competitions for Aston Villa this season.
Jansson, who will join Malmo in the summer from Brentford, considers Olsen one of the best players in Sweden and wants to lure him and Emil Forsberg back home, to Malmo.
“Many people wonder how many ‘homecomers’ you can have, but when we’re talking about Sweden’s most influential players on the national team, as Robin and Emil are, it’s clear that they should come home at all costs if they want to and feel ready”, Jansson told Swedish outlet Fotbollskanalen.
“We’re talking about some of the best players in Sweden, and as a part of the Malmo squad now and with my love for Malmo, I will of course do everything I can to get them to come home.”
The Brentford defender also stated that he is confident that the Aston Villa star will go back to Sweden to join his boyhood club, with the two friends sure to be reunited.
“I’m sure about Robin”, he added.
“He’s a Malmo boy and he’s my closest footballing friend.
“He has no choice.
“He’s going home and that’s that.”
Malmo’s 2023 season in the Swedish top flight is ongoing and they currently sit top of the table, having won eight and drawn one of their nine games so far.