The Heart want the LA Galaxy midfielder in Melbourne on an initial 10-game guest stint which is likely to be worth in excess of $1million.
"We are incredibly serious and working tirelessly with David's representatives to table a compelling offer which is commensurate with the international player that David is," Munn told BBC Sport.
"We're taking to David about a 10-game stint.
"Football is the third code behind Australian Rules football and rugby league - we think David takes it to the next level."
Beckham, who has also recently been linked with French giants Paris Saint-Germain as well as other A-League clubs Perth Glory, Central Coast Mariners and Adelaide United, is preparing for his final match with the Galaxy â€“ the MLS Cup final against Houston Dynamo on December 1.