The Red Dragons want to make better use of the stadium and will meet Welsh Government members in Cardiff to state their case.
Plans include an idea to house a national art museum and national football museum at their base.
Director Spencer Harris wants the club's ground to help generate non-matchday funds for Wrexham.
Spencer said:"There is a fantastic opportunity here for the leaders of our national government to help us create something the region can be proud of.
"The Racecourse can serve the needs of north and mid Wales and deliver sporting and cultural accessibility to all parts of the country.
"We have had a very positive reaction from both the local authority and Glyndwr University and hope to build on that momentum with Welsh Government."
He added in a statement: "As north-east Wales is the only part of the country without a national museum and, with Wrexham being the birthplace of football in Wales, it is a logical solution to locate a museum at the Racecourse Ground as part of a wider development of the stadium."