The Dragons stand-off, who has played 27 tests for New Zealand, met with Scotland coach Steve McCormack in June, according to reports.
According to Rugby League Week, 30-year-old Marshall has Scottish ancestry.
McCormack is attempting to attract big names to Scotland ahead of the European Cup at the end of the year.
If he does don the Scottish blue jersey it might not be long before Marshall plays against New Zealand with Scotland taking part in next year's Four Nations tournament.
Marshall has fallen out of favour with the Kiwis following his brief rugby stint with the Blues last season.
Coach Stephen Kearney has opted for the younger halves combination of Shaun Johnson and Kieran Foran which has resulted in a Four Nations title and an Anzac test victory in the last eight months.
