Jenna Ushkowitz has also been linked to co-star Kevin McHale, but Michele reveals none of the stars of the show are romancing each other - and she's glad.
She tells Britain's Cosmopolitan magazine, "(The public) thinks that everyone is sleeping with everyone. We spend every minute of every day together, and when we're finished we all go out to dinner, so of course they think we're hooking up.
"I'm thankful that it doesn't happen. If people hooked up, there'd be awkward tensions."
And Morrison echoes Michele's sentiments, adding, "I think it's funny... but it's a little embarrassing because they're supposedly my students. And I hear a rumour of me hooking up with one of them and I'm like, 'Eeeww!' I once dated someone that I was in a show with and these things never end well. It's best to keep it professional."