The Sunday Mirror says Wenger has been assured that he will have £35million-plus to invest in new players during the January transfer window.
The Arsenal manager will be able to use the profits announced by the club last week.
“If Arsene wants to use that money during the winter window then, absolutely, he will be able to do it,” said chairman Peter Hill-Wood.
“We rely on him to come up with the right people and there will be funds available to him.
“We have been very pleased with the start.
“But if the manager wants to reinforce the squad in January, he will be able to do that."