Having completed the sale of Wilfried Bony to Manchester City for £28 million, the Swans have cash to spare and Monk will presumably use it to bolster his squad.
They have already made approaches to the Canaries about the left-back, but those have been rejected by the club. Despite that, it is believed Swansea will push ahead with their interest in the player.
Olsson has been at Carrow Road since 2013 but is thought to want a return to the top flight should it become available. Norwich are currently 8th in the Championship, eight points off an automatic promotion place.
Monk is also having trouble signing Tottenham full back Kyle Naughton according to the newspaper.
Naughton is free to leave White Hart Lane as he is not in manager Mauricio Pochettino’s long-term plans. That has alerted Swansea, who are keen to make a move happen. The paper also credits Leicester City with an interest in his services.