Can I claim my elderly parents as dependents without jeopardizing their Medicare benefits?

Medicare or MEDICAID? There's a big difference. If they get MEDICAID, claiming them would be a real SNAFU. Also be aware that IRS wants them to be with you for 12 months and prove you provide more than half of their support. This is one of those things that triggers an audit. Your call.

They are on currently receiving Medicare.

I think there is reason for pause here if only because by claiming them as dependents you are saying basically that you use your income (assets) to pay for their care. But do you also take over control of the proceeds of their monthly Social Security benefits, and would this then be construed as additional income, based on the existing formula, that must be reported on your tax forms. Wow! When I started to answer your question I certainly wasn't going HERE! I hate to say this but it sounds like this may need to be attended to by a professional...or one of the many helpful people on this site who know so much about this stuff, either because it's their job or because they've been down this road themselves with their parents. Good luck to you, I'll be watching for the advice you get.

Thank you very much

This is easy. Your question was will this affect their Medicare benefits. The answer is no. They have earned and paid into Medicare and it is theirs. They aren't going to lose it. Medicare (and Social Security) are not based on need. They are benefits the recipient has already earned. They are different from SSI and Medicaid which are both needs based. Don't overthink this.

Claiming certain persons as dependents do not necessarily require that person to live with you, or even the full 12 months of the year. A parent of a taxpayer can be considered a dependent based on providing over half of their financial support, including the FMV of direct care, I you had to pay someone to perform those same services on their behalf. The residency requirement does not apply to adult parents the same way it could apply to certain other relatives. Check Pub. 17 for guidance and referral to other IRS Pubs regarding the dependent exemption.