You are able to connect your One account to any budgeting tool that utilized the Plaid exchange network. At this time, Mint.com does not utilize Plaid.
Instead, Mint.com prioritizes adding financial institutions based on the demands of their customer base. If you're open to it, they ask that their users message them directly using this format.
If there is anything we can do to support you in your reach out to them, let us know by submitting a request here.