Bruce Crawford, whose constituency includes Blanefield, Stirlingshire, will ask Mr Swinney to pledge funding towards the overall cost which is estimated at around £630,000. It comes after the UK Government said it would provide £255,000 to help clear up the land, which has traces of industrial pollution.
Stirling Council has offered to pay £125,000 and its leader, Johanna Boyd, said she was hopeful the meeting would relieve the "huge burden" on residents.
The Scottish Government has said it would look at ways to help.
Stirling Council deputy leader Neil Benny said: "This has been a tremendous stress on the residents of Blanefield and we hope and pray our local MSP is successful."