I have never tried to do as you desire but do know that at MINT (mint.com) you can download your transactions to a csv file. With a software tool you could take the csv file and put it in a format that could be used to transfer the transactions to Quicken. Here is a link to a software tool as I mention. http://www.quicknperlwiz.com/
I would like to mention that because there is no way to get your transactions entered into Quicken into Mint this is not a "sync" it is a one way transfer of transactions from Mint to Quicken. Also Mint export to a CSV file has no time range on it, so it is not really good for an on going download either. So the best use would be for a one time dump from Mint to Quicken. Or I know one person that basically used as a remote input. He put transactions into Mint during a vacation and downloaded them into Quicken after the trip.