The midfielder, 29, has another year left to run on his Potters' deal but has been on the radar of Moyes' Real Sociedad.
However, the Scotland ace admits he is keen to spend his best remaining years at the Britannia Stadium.
He said: "I love it at Stoke. It's a great club. Some people think I'm going to go at the end of the season. I'm not going anywhere, I still have another year to go on my contract.
I will see it out and if the club want to speak to me about a new contract I would be delighted to sign
Charlie Adam
"I will see it out and if the club want to speak to me about a new contract I would be delighted to sign.
"The fans are great, they have a good manager in Mark Hughes and hopefully I can stay here for many years.
"Real Sociedad play in the top league in Spain and he's done a great job there but I have a Stoke contract and am happy here until told otherwise.
"I have been here nearly three years now and hopefully I will continue here for many yeas to come after my contract is up."
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