The Frenchman began his career in the principality and won two trophies in a seven-year spell that ended with his sacking in 1994.
Monaco faced the Gunners in the Emirates Cup in July, and Vasilyev hopes that Wenger's "strong affection" for the Ligue 1 outfit is enough to make him return in the future.
"For Monaco he is part of our history, part of our heritage," the Russian chief is quoted as saying by the Daily Mail.
"He is doing an amazing job. I don't know if one day he will want to come back, but we keep a very good relationship.
"Last time we exchanged was during the Emirates Cup. He keeps a strong affection for Monaco."
The 64-year-old is contracted until 2017 after signing a three-year extension in May, having guiding the club to FA Cup success - their first trophy since 2005.
Wenger, who joined the North Londoners in 1996, is not believed to have ever broken a contract during his 30-year managerial career.