Martin's reported contract demands could test Penrith's salary-cap discipline, though he is understood to prefer staying.
The 29-year-old wants a three-year extension worth about $1 million annually, up from his current $750,000 salary.
Off contract after 2027, he can negotiate elsewhere from November 1 if Penrith has not secured him.
NewsCorp reports Cronulla and Brisbane are interested in signing the four-time Panthers premiership winner for 2028.
Martin has also represented New South Wales and Australia.
At Cronulla, Briton Nikora and Teig Wilton are off-contract in 2027.
At Brisbane, Brendan Piakura is off-contract in a year, while Xavier Willison is reportedly linked with an exit after 2027.
Broncos assistant coach Trent Barrett, Martin's cousin, may give Brisbane an existing connection.
Penrith CEO Matt Cameron outlined the club's approach on the Bye Round podcast earlier this year.
"We talk about making disciplined salary cap decisions."