News of the offer came via Sky Sports News' Blake Welton, who said the Toffees are likely to come back with an increased bid for the 23-year-old before the transfer deadline closes on Thursday at 5 p.m. (BST).
The story was confirmed by BBC Sport's David Ornstein, who added that Everton are seeking to sign Iwobi in addition to Crystal Palace winger Wilfried Zaha:
David OrnsteinAs per others, Everton £30m bid for Alex Iwobi rejected. Made to Arsenal today & knocked back. Expected to return with improved offer but likely need £40m+ to be accepted.