Edelman told BBC Radio Five Live Sportsweek: "We'd like Arsene to be with the club for a very long time, but he'll have to look at what he wants to do as well.
"We are generating more money out of Emirates Stadium than our debt repayment.
"Therefore we are more profitable at Emirates than we were at Highbury and therefore we can invest more money.
"We will have the largest gate revenue in the UK and when our results are produced (in September) and you see the amount of cash the business has got, some of the comments that have been made over the summer are very wide of the mark.
"We're in very, very good financial health and we're financially very strong as a club."