BBC Sport says Arsenal have made an enquiry for the Belgium midfielder this week.
It's suggested Everton will sell this summer at a starting price of £50 million.
Onana is preparing for the Euros kick-off and said last week: "In previous tournaments you have seen that the players who did well take the step higher to the top clubs.
"That's something I'm striving for. I feel like showing myself at the European summit. This European Championship is the stage."