Eagles has been in impressive form for the Clarets this season and his brace against Barnsley last week was watched by Toffees boss David Moyes.
The 24-year-old turned down the chance to join Rangers in the summer and subsequently committed his future to Burnley by signing a new two-year contract.
Laws is not concerned that Premier League clubs will be taking note of Eagles' form and is confident the former Manchester United youngster is happy at Turf Moor.
"I think the time to worry was in the summer, but that's all behind us now," said Laws. "He's signed a new contract, he's here for the next few years.
"He's settled. He went to Rangers and had a chat with them - we wanted him to have a look at it - because we know that if he's happy he'll play where he's happy.
"He's definitely happy here. You can see that in his performances and in himself.
"That doesn't worry me one bit. If people are watching him, great.
"That means he's in top form, it means we're doing something right and we'll get the benefits from it."