According to The Australian, the Sharks contacted Munster’s management last season and were told that they were one of only three clubs he would consider playing for beyond 2019.
The other two clubs appear to be Melbourne and the Sydney Roosters.
Munster has a year remaining on his current contract with the Storm, who are set to table a multi-million dollar deal to keep him at the club.
However the prospect of playing full back is believed to be attracting Munster to the Sharks.
Sharks coach Shane Flanagan is a known admirer of the 24-year-old and spent yesterday explaining the challenge of shutting down the Melbourne star.
“Last time we played against them he had a hand in one or two tries, including one from the kick,” Flanagan said in a press conference.
“Sometimes, when things look like they are all shut down, he has really good footwork and a fend. He can create something from nothing. So he will creep across the field … just find space and push his nose through. We have to be good on that.”
“He has had a fantastic year and he is one of the players we have spoken about consistently all week. He can stick to structure and when he is most dangerous, it is when he is doing something off the top of his head.”
Munster leads the Storm for in try assists and line break assists this season, having 29 across the two categories.
Munster will line-up against the Sharks in Friday night’s preliminary final at AAMI Park.