The Glaswegian pair, two of the Barclays Premier League's six managers born in Scotland, face each other as the Toffees travel to the Reebok Stadium.
It is Moyes' record over almost nine years at Goodison Park, which includes a fourth-place finish and an FA Cup final appearance, that impresses Coyle.
Moyes said: "It's very kind of him but there are a lot of young, promising managers out there who would like to be given opportunities and I am sure if Owen keeps doing what he is doing, he'll be competing at the highest level.
"He already is with what he is doing at Bolton - he will be pleased with the way it is going.
"His team are playing great. He took them over in a really difficult position last year and got them away from relegation. He has had a great year in the job, done really well."
Source: PA
Source: PA